Expert-Mediated Search

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Expert-Mediated Search"

Transcription

1 Exprt-Mdiatd Sarch Mnal Chhabra Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA Sanmay Das Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA David Sarn Bar-Ilan Univrsity Dpt. of Computr Scinc Ramat Gan, Isral ABSTRACT Incrasingly in both traditional, and spcially Intrnt-basd marktplacs, knowldg is bcoming a tradd commodity. This papr considrs th impact of th prsnc of knowldgbrokrs, or xprts, on sarch-basd markts with noisy signals. For xampl, considr a consumr looking for a usd car on a larg Intrnt marktplac. Sh ss noisy signals of th tru valu of any car sh looks at th advrtismnt for, and can disambiguat this signal by paying for th srvics of an xprt (for xampl, gtting a Carfax rport, or taking th car to a mchanic for an inspction). Both th consumr and th xprt ar rational, slf-intrstd agnts. W prsnt a modl for such sarch nvironmnts, and analyz svral aspcts of th modl, making thr main contributions: (1) W driv th consumr s optimal sarch stratgy in nvironmnts with noisy signals, with and without th option of consulting an xprt; (2) W find th optimal stratgy for maximizing th xprt s profit; (3) W study th option of markt dsignrs to subsidiz sarch in a way that improvs ovrall social wlfar. W illustrat our rsults in th contxt of a plausibl distribution of signals and valus. Catgoris and Subjct Dscriptors J.4 [Social and Bhavioral Scincs]: Economics Gnral Trms Algorithms, Economics Kywords Economically-motivd agnts, Modling th dynamics of MAS 1. INTRODUCTION In many multi-agnt systm (MAS) sttings, agnts ngag in on-sidd sarch [13, 6]. This is a procss in which an agnt facs a stram of opportunitis that aris squntially, and th procss trminats whn th agnt picks on of thos opportunitis. A classic xampl is a consumr looking to buy a usd car. Sh will typically invstigat cars on at a tim until dciding upon on sh wants. Similar sttings Cit as: Exprt-Mdiatd Sarch, Mnal Chhabra, Sanmay Das, and David Sarn, Proc. of 1th Int. Conf. on Autonomous Agnts and Multiagnt Systms (AAMAS 211), Tumr, Yolum, Sonnbrg and Ston (ds.), May, 2 6, 211, Taipi, Taiwan, pp. XXX-XXX. Copyright c 211, Intrnational Foundation for Autonomous Agnts and Multiagnt Systms ( All rights rsrvd. can b found in job-sarch, hous sarch and othr applications [12, 15]. In modrn lctronic marktplacs, sarch is likly to bcom incrasingly important as, with th prolifration of possibl sllrs of a good, consumrs will turn to artificial agnts, whom w trm sarchrs, to find th bst prics or valus for itms thy ar intrstd in acquiring. Th dcision making complxity in on-sidd sarch usually ariss from th fact that thr is a cost incurrd in finding out th tru valu of any opportunity ncountrd. For xampl, thr is a cost to arranging a mting to tst driv a car you ar considring purchasing. Th sarchr thus nds to trad off th potntial bnfit of continuing to sarch and sing a mor valuabl opportunity with th costs incurrd in doing so. Th optimal stopping rul for such sarch problms has bn widly studid, and is oftn a rsrvation stratgy, whr th sarchr should trminat sarch upon ncountring an opportunity which has a valu abov a crtain rsrvation valu or thrshold [18, 13]. Most modls assum that th sarchr obtains th xact tru valu of th opportunitis it ncountrs. Howvr, in many ralistic sttings, sarch is inhrntly noisy and sarchrs may only obtain a noisy signal of th tru valu. For xampl, th drivtrain of a usd car may not b in good condition, vn if th body of th car looks trrific. Th rlaxation of th assumption of prfct valus not only changs th optimal stratgy for a sarchr, it also lads to a nich in th marktplac for nw knowldg-brokrs. Th knowldg brokrs, or xprts, ar srvic providrs whos main rol is to inform consumrs or sarchrs about th valus of opportunitis. An xprt offrs th sarchr th option to obtain a mor prcis stimat of th valu of an opportunity in qustion, in xchang for th paymnt of a f (which covrs th cost of providing th srvic as wll as th profit of th xprt). To continu with th usd car xampl, whn th agnt is intrigud by a particular car and wants to larn mor about it, sh could tak th car to a mchanic who could invstigat th car in mor dtail to mak sur it is not a lmon. Th xprt nd not b a mchanic it could b, for xampl, an indpndnt agncy, lik Carfax, that monitors th rcordd history of transactions, rpairs, claims, tc. on cars. It can also b a rpatd visit of th sarchr to s th car, possibly bringing an xprincd frind for a mor thorough xamination. In all ths cass, mor accurat information is obtaind for an additional cost (ithr montary or quivalnt). In this papr w invstigat optimal sarch and mchanism dsign in nvironmnts whr sarchrs obsrv noisy signals and can obtain (i.., qury th xprt for) th ac-

2 tual valus for a f. Our main contributions ar thrfold: First, w introduc a spcific modl of on-sidd sarch with noisy signals and prov that th optimal sarch rul, for a larg class of ral-lif sttings, is rsrvation-valu basd. Scond, w formally introduc th option of consulting an xprt in such noisy sarch nvironmnts, and driv th optimal stratgy for th sarchr givn a cost of consulting th xprt, as wll as th profit-maximizing pric for th xprt to charg for its srvics. As part of th analysis w prov that undr th standard assumption that highr signals ar good nws (i.., th distribution of th tru valu conditional on a highr signal stochastically dominats th distribution conditional on a lowr signal), th optimal sarch stratgy is charactrizd by a doubl rsrvation valu stratgy, whrin th sarchr rjcts all signals blow a crtain thrshold, rsuming sarch, and accpts all signals abov anothr thrshold, thus trminating sarch, without qurying th xprt; th agnt quris th xprt for all signals that ar btwn th two thrsholds. Finally, w study a markt dsign mchanism (introduction of a subsidy) with th potntial to improv social wlfar in such domains. Ths mchanisms may b implmntd by ithr an lctronic marktplac that mploys th xprt (for xampl a wbsit for usd cars that has a rlationship with a providr of car history rports), or an ntity with rgulatory powr lik th govrnmnt. Along with th gnral thory, w illustrat our rsults in a spcific, plausibl distributional modl, in which th tru valu is always boundd by th signal valu, and th probability monotonically dcays as th discrpancy btwn th two incrass. 2. THE GENERAL MODEL Th standard on-sidd sarch problm [13] considrs an agnt or sarchr facing an infinit stram of opportunitis from which sh nds to choos on. Whil th spcific valu v of ach futur opportunity is unknown to th sarchr, sh is acquaintd with th (stationary) probability distribution function from which opportunitis ar drawn, dnotd f v(x). Th sarchr can larn th valu of an opportunity for a cost c s (ithr montary or in trms of rsourcs that nd to b consumd for this purpos) and hr goal is to maximiz th nt bnfit, dfind as th valu of th opportunity vntually pickd minus th ovrall cost incurrd during th sarch. Having no a priori information about any spcific opportunity, th sarchr rviws th opportunitis sh ncountrs squntially and sts hr optimal stopping rul. Th stopping rul spcifis whn to trminat and whn to rsum sarch, basd on th opportunitis ncountrd. Our modl rlaxs th standard assumption that th sarchr rcivs th xact tru valu of an opportunity. Instad, w assum that th sarchr rcivs, at cost c s, a noisy signal s, corrlatd with th tru valu according to a known probability dnsity function f s(s v). In addition, th sarchr may qury and obtain from a third party (th xprt) th tru valu v of an opportunity for which signal s was rcivd, by paying an additional f c. Th goal of th sarchr is to maximiz th total utility rcivd i.., th xpctd valu of th opportunity vntually pickd minus th xpctd cost of sarch and xprt fs paid along th way. Th first qustion that ariss is how to charactriz th optimal stratgy for th sarchr. A scond qustion is how th xprt sts hr srvic f c. In this papr w considr a monopolist providr of xprt srvics. Th sarchr s optimal stratgy is dirctly influncd by c, and thus implicitly dtrmins th xpctd numbr of tims th srvics of th xprt ar rquird, and thus th xprt s rvnu. Th problm can b thought of as a Stacklbrg gam [5] whr th xprt is th first movr, and wants to maximiz hr profits with rspct to th f c sh chargs sarchrs. Th nw sarch modl raiss intrsting nw qustions about markt dsign. Assuming xognity of opportunitis, social wlfar, dnotd W, is a function of th xpctd valu to sarchrs and th xpctd profit of th xprt. (W abstract away from modling th xistnc of sllrs of opportunitis, instad viwing thm as xognous, or ls as bing offrd at som fair pric by th sllr.) W assum that th providr of xprt srvics has alrady prformd th startup work ncssary, and only pays a marginal cost d pr qury, and that social wlfar is additiv. Sinc th procss scals up linarly in th numbr of sarchrs, w can simply considr th intractions involving a singl sarchr and th xprt. Th social wlfar is thn th sum of th xpctd nt bnfit to th sarchr and th xpctd profit of th xprt. It turns out that social wlfar can b significantly affctd (and improvd) if th markt dsignr (or a rgulator lik th govrnmnt) subsidizs quris by compnsating th xprt in ordr to rduc qury costs to th sarchr. W now turn to dvloping th mathmatical machinry to addrss ths problms. 3. OPTIMAL POLICIES In this sction, w analyz th sarchr s optimal sarch stratgy and hr xpctd us of th xprt s srvics, givn th f c st by th xprt. Th analysis builds on th trivial non-noisy modl and gradually adds th complxitis of signals and having th xprt option. From th sarchr s optimal sarch stratgy w driv th xprt s xpctd bnfits as a function of th f sh sts, nabling maximization of th xprt s rvnu. On-Sidd Sarch. Th optimal sarch stratgy for th standard modl, whr th actual valu of an opportunity can b obtaind at cost c s, can b found in th xtnsiv litratur of sarch thory [13, 6]. In this cas, th sarchr follows a rsrvation-valu rul: sh rviws opportunitis squntially (in random ordr) and trminats th sarch onc a valu gratr than a rsrvation valu x is rvald, whr th rsrvation valu x satisfis: c s = y=x (y x )f v(y)dy (1) Intuitivly, x is th valu whr th sarchr is prcisly indiffrnt: th xpctd marginal bnfit from continuing sarch and obtaining th valu of th nxt opportunity xactly quals th cost of obtaining that additional valu. Th rsrvation proprty of th optimal stratgy drivs from th stationarity of th problm rsuming th sarch placs th sarchr at th sam position as at th bginning of th sarch [13]. Consquntly, a sarchr that follows a rsrvation valu stratgy will nvr dcid to accpt an opportunity sh has onc rjctd and th optimal sarch stratgy is th sam whthr or not rcall is prmittd. Th xpctd numbr of sarch itrations is simply th invrs of th succss probability,, sinc this bcoms a Brnoulli 1 1 F v(x )

3 sampling procss, as opportunitis aris indpndntly at ach itration. On-Sidd Sarch with Noisy Signals. Bfor bginning th analysis of sarch with noisy signals, w mphasiz that, givn f v(x) and f s(s v), w can also driv th distribution of th signal rcivd from a random opportunity, f s(x), and th distribution of tru valus conditional on signals, f v(v s) (th conditionals ar intrchangabl by Bays law). In many domains, it may b asir to assss/larn f s(s) than f v(v s) as most past xprinc involvs signals, with th actual valu rvald for only a subst of ths signals. Whn th sarchr rcivs a noisy signal rathr than th actual valu of an opportunity, thr is no guarant that th optimal stratgy is rsrvation-valu basd as in th cas whr valus obtaind ar crtain. Indd, th stationarity of th problm still holds, and an opportunity that has bn rjctd will nvr b rcalld. Yt, in th absnc of any rstriction ovr f s(s v), th optimal stratgy is basd on a st S of signal-valu intrvals for which th sarchr trminats th sarch. Th xpctd valu in this cas, dnotd V (S), is givn by: V (S) = c s + Pr(s / S)V (S) + P r(s S)E[v s S] = c s + V (S) f s(s) ds + f s(s)e[v s] ds (2) s / S s S Th fact that th optimal stratgy may not b rsrvationvalu basd in this cas is bcaus thr may b no corrlation btwn th signal and th tru valu of th opportunity. Nvrthlss, in most ral-lif cass, thr is a natural corrlation btwn signals and tru valus. In particular, a fairly wak and commonly usd rstriction on th conditional distribution of th tru valu givn th signal gos a long way towards allowing us to rcaptur a simpl spac of optimal stratgis. This is th rstriction that highr signal valus ar good nws in th sns that whn s 1 > s 2, th conditional distribution of v givn s 1 first-ordr stochastically dominats that of v givn s 2 [19, 14]. Th condition rquirs that givn two signals s 1 and s 2 whr s 1 > s 2, th probability that th actual valu is gratr than any particular valu v is gratr for th cas whr th sarchr rcivs signal s 1. Formally: Dfinition 1. Highr signals ar good nws (HSGN) assumption: If s 1 > s 2, thn, y, F v(y s 1) F v(y s 2). This nabls us to prov th following thorm. Thorm 1. For any probability dnsity function f v(v s) satisfying th HSGN assumption, th optimal sarch stratgy is a rsrvation-valu rul, whr th rsrvation valu, t, satisfis: ( ) c s = E[v s] E[v t ] ds (3) s=t Proof: Th proof is basd on showing that, if according to th optimal sarch stratgy th sarchr should rsum hr sarch givn a signal s, thn sh must ncssarily also do so givn any othr signal s < s. Lt V dnot th xpctd bnfit to th sarchr if rsuming th sarch. Sinc th optimal stratgy givn signal s is to rsum sarch, w know V > E[v s]. Givn th HSGN assumption, y yfv(y s ) dy < yfv(y s) dy holds for y s < s. Thrfor, V > E[v s ], proving that th optimal stratgy is rsrvation-valu. Thn, th xpctd valu of th sarchr whn using rsrvation signal t is givn by: t V (t) = c s + V (t) f s(s) ds + E[v s]f s(s) ds s= s=t = cs + E[v s]fs(s) ds s=t (4) 1 F s(t) whr F s(s) is th cumulativ distribution function of th signal s. Stting th first drivativ according to t of Equation 4 to zro w obtain: V (t ) = E[v t ]. Th scond drivativ for t that satisfis th lattr quality confirms that this is indd a global maximum. Finally, using intgration by parts ovr th drivativ according to t of Equation 4 w obtain Equation 3, and th valu t can b calculatd accordingly. Th social wlfar W is th xpctd gain to th sarchr from following th optimal stratgy, V (t ) = E[v t ]. Th xpctd numbr of sarch itrations is is a Brnoulli sampling procss. 1 1 F s(t ), sinc this Th Exprt Option. Th introduction of an xprt xtnds th numbr of dcision altrnativs availabl to th sarchr. Whn rciving a noisy signal of th tru valu, sh can choos to (1) rjct th offr without qurying th xprt, paying sarch cost c s to rval th signal for th nxt offr; (2) qury th xprt to obtain th tru valu, paying a cost c, and thn mak a dcision; or (3) accpt th offr without qurying th xprt, rciving th (unknown) tru valu of th offr. In cas (2), thr is an additional dcision to b mad, whthr to rsum sarch or not, aftr th tru valu v is rvald. As in th no-xprt cas, a solution for a gnral dnsity function f v(v s) dictats an optimal stratgy of a complx structur. In our cas, th optimal stratgy will hav th form of (S, S, V ), whr: (a) S is a st of signal intrvals for which th sarchr should rsum hr sarch without qurying th xprt; (b) S is a st of signal intrvals for which th sarchr should trminat hr sarch without qurying th xprt (and pick th opportunity associatd with this signal); and (c) for any signal that is not in S or S th sarchr should qury th xprt, and trminat th sarch if th valu obtaind is abov a thrshold V, and rsum othrwis. Th valu V is th xpctd bnfit from rsuming th sarch and is givn by th following modification of Equation 2: V = c s + V f s(s) ds c s S ( V f s(s) V f v(x s) dx+ s {S,S } x=v s {S,S } f s(s) ds+ ) xf v(x s) dx ds + f s(s)e[v s] ds (5) s S Th first lmnt on th right hand sid of th quation applis to th cas of rsuming sarch, in which cas th sarchr continus with an xpctd bnfit V. Th scond lmnt is th xpctd paymnt to th xprt. Th nxt lmnts rlat to th cas whr th sarch is rsumd basd on th valu rcivd from th xprt (in which cas th xpctd rvnu is onc again V ) and whr th sarch is

4 trminatd (with th valu E[v s] obtaind as th rvnu), rspctivly. Finally, th last lmnt applis to th cas whr th sarchr trminats th sarch without qurying th xprt. W can show that undr th HSGN assumption, ach of th sts S and S actually contains a singl intrval of signals, as illustratd in Figur 1. Thorm 2. For f v(y s) satisfying th HSGN assumption (Dfinition 1), th optimal sarch stratgy can b dscribd by th tupl (t l, t u, V ), whr: (a) t l is a signal thrshold blow which th sarch should b rsumd; (b) t u is a signal thrshold abov which th sarch should b trminatd and th currnt opportunity pickd; and (c) th xprt should b qurid givn any signal t l < s < t u and th opportunity should b accptd (and sarch trminatd) if th valu obtaind from th xprt is abov th xpctd valu of rsuming th sarch, V, othrwis sarch should rsum (s Figur 1). Th valus t l, t u and V can b calculatd from solving th st of Equations 6-8: x=v tl tu V = c s + V f s(s) ds c f s(s) ds+ s= s=t l tu ( V f s(s) V f v(x s) dx ds+ s=t l x= ) xf v(x s) dx ds + f s(s)e[v s] ds (6) s=t u c = c = y=v V (y V )f v(y t l ) dy (7) (V y)f v(y t u) dy (8) Proof: Th proof xtnds th mthodology usd for proving Thorm 1. W first show that if, according to th optimal sarch stratgy th sarchr should rsum hr sarch givn a signal s, thn sh must also do so givn any othr signal s < s. Thn, w show that if, according to th optimal sarch stratgy th sarchr should trminat hr sarch givn a signal s, thn sh must also ncssarily do so givn any othr signal s > s. Again, w us V to dnot th xpctd bnfit to th sarchr if rsuming th sarch. If th optimal stratgy givn signal s is to rsum sarch thn th following two inqualitis should hold, dscribing th supriority of rsuming sarch ovr trminating sarch (Equation 9) and qurying th xprt (Equation 1): V > E[v s] (9) V > c + y=v yf v(y s) dy + V V y= f v(y s) dy (1) Givn th HSGN assumption and sinc s < s, Equation 9 holds also for s, and so dos Equation 1 (which can b formalizd aftr som mathmatical manipulation as: V > c + V + (y V )fv(y s) dy). Th proof for y=v s > s is similar: th xpctd cost of accpting th currnt opportunity can b shown to dominat both rsuming th sarch and qurying th xprt. W omit th dtails bcaus of spac considrations. Th optimal stratgy can thus b dscribd by th tupl (t l, t u, V ) as statd in th Thorm. Thrfor, Equation 5 transforms into Equation 6. Taking th drivativ of Equation 6 w.r.t. t l and quating to zro, w obtain a uniqu t l which maximizs th xpctd bnfit (vrifid by scond drivativ), and similarly for t u. Finally, using intgration by parts ovr th drivativs of Equation 6 w.r.t. t l and t u w obtain Equations 7-8. Intuitivly, t l is th point at which a sarchr is indiffrnt btwn ithr rsuming th sarch or qurying th xprt and t u is th point at which a sarchr is indiffrnt btwn ithr trminating th sarch or qurying th xprt. Th cost of purchasing th xprt s srvics must qual two diffrnt things: (1) th xpctd savings from rsuming th sarch whn th actual utility from th currnt opportunity (which is not known) turns out to b gratr than what can b gaind from rsuming th sarch (onc it is rvald) (this is th condition for t l ); (2) th xpctd savings from trminating th sarch in thos cass whr th actual utility from th currnt opportunity (onc rvald) is lss than what can b gaind from rsuming th sarch (for t u). Figur 1: Charactrization of th optimal stratgy for noisy sarch with an xprt. Th sarchr quris th xprt if s [t l, t u] and accpts th offr if th worth is gratr than th valu of rsuming th sarch V. Th sarchr rjcts and rsums sarch if s < t l and accpts and trminats sarch if s > t u, both without qurying th xprt. It is notabl that thr is also a rasonabl dgnrat cas whr t l = t u(= t). This happns whn th cost of qurying is so high that it nvr maks sns to ngag th xprt s srvics. In this cas, a dirct indiffrnc constraint xists at th thrshold t, whr accpting th offr yilds th sam xpctd valu as continuing sarch, so V = E[v t]. This can b solvd in combination with Equation 4, sinc thr ar now only two rlvant variabls. Expctd numbr of quris: Th sarch stratgy (t l, t u, V ) dfins how many tims th xprt s srvics ar consultd. In ordr to comput th xpctd numbr of quris, w considr four diffrnt typs of transitions in th systm. Lt A b th probability that th sarchr quris th xprt and thn dos not accpt, rsuming sarch, B b th probability that th sarchr rsums sarch without qurying, C b th probability that th sarchr trminats without qurying, and D b th probability that th sarchr quris th xprt and trminats sarch. Thn: A = Pr(t l s t u and v < V ) (11) B = Pr(s < t l ) (12) C = Pr(s > t u) (13) D = Pr(t l s t u and v V ) (14) Lt P j dnot th probability that th sarchr quris th xprt xactly j tims bfor trminating. Th sarchr can trminat sarch aftr xactly j quris in on of two ways: ithr sh maks j 1 quris, thn quris th xprt and chooss to trminat, or sh maks j quris and

5 thn chooss to trminat without qurying th xprt. Factoring in all th possibl ways of intrlaving j quris with an arbitrary numbr of tims that th sarchr chooss to continu sarch without qurying th xprt, w gt: P j = = m= (m + j 1)! m!(j 1)! A j (1 B) j ( D A + C 1 B ) A j 1 B m D + m= (m + j)! A j B m C m!j! Thn th xpctd numbr of quris, whn charging an xprt f c, is givn by j= jpj, yilding η c = E(Numbr of quris c ) = (1 B)D + CA (1 B A) 2 (15) Expctd numbr of opportunitis xamind: Using th sam notation as abov, w s that th probability of trminating th sarch at any itration is C + D, and ths ar indpndnt Brnoulli draws at ach opportunity. Thrfor th xpctation of th numbr of opportunitis xamind is simply η s = 1/(C + D). Expctd profit of th xprt: Lt d dnot th marginal cost of th srvic th xprt is providing. Th xpctd profit of th xprt is thn simply π = E(Profit) = (c d )η c Th xprt can maximiz th abov xprssion with rspct to c (η c dcrass as c incrass) to find th profit maximizing pric to charg sarchrs. Social Wlfar: Th social wlfar is givn by th sum of all partis involvd, thus far just th sarchr and th xprt. Of cours this gnralizs to multipl agnts as wll, sinc ach sarch procss would b indpndnt. W dfin: W = V c + π (16) whr c is th f that maximizs th xprt s profit. 4. MARKET DESIGN Abov, w hav dscribd th basics of sarch in such xprt-mdiatd markts. In this sction, w dscrib possibl uss of th thory dscribd abov to improv th dsign of markts in which such sarch taks plac. Th prospct of dsigning or significantly influncing ths markts is not rmot. Considr th dsign of a larg scal Intrnt wbsit lik autotradr.com. Th listings for cars that usrs s ar signals, and thy may b unsur of a car s tru worth. autotradr can partnr with a providr of rports lik Carfax, to mak it asy for usrs to look up a car s worth. In ordr to b gnral, lt us rfr to autotradr as th markt (or in som instancs as th markt dsignr ) and Carfax as th xprt. Th markt wants to attract customrs to it, rathr than to rival markts. Th bst way of doing this is to provid customrs with a high valu shopping xprinc. Th xprt wishs to maximiz its profits. Sinc th markt and th xprt both hav significant powr, it is rasonabl to imagin thm coming up with diffrnt modls of th kinds of rlationships thy may hav. It is notabl that whil w ar thinking about privat markts hr, this ntir discussion is qually rlvant to a big playr lik th govrnmnt as markt dsignr, and indpndnt providrs of xprt srvics. In ordr to provid customrs with th highst valu shopping xprinc, th markt may choos to subsidiz th cost of xprt srvics. A typical problm with subsidization is that it oftn dcrass social wlfar bcaus th tru cost of whatvr is bing subsidizd is hiddn from th consumr, lading to ovrconsumption of th rsourc. In this instanc, howvr, th natural xistnc of many monopolis in xprt srvics, combind with th xistnc of sarch frictions, mak it quit possibl that subsidis will in fact incras social wlfar. W show in Sction 5 that this is in fact th cas for som natural distributions. Th basic framwork of subsidization works as follows. Suppos a monopolist providr of xprt srvics maximizs its profits by stting th qurying cost to c, yilding an xpctd profit π = (c d )η c (this discussion is on a pr-consumr basis). Th markt dsignr can stp in and ngotiat a rduction of th f c chargd by th xprt, for th bnfit of th agnts. In rturn for th xprt s agrmnt, th markt dsignr will nd to offr a pr-consumr paymnt β to th xprt, which fully compnsats th xprt for th dcrasd rvnu, laving hr total profit th sam. Sinc c < c, η > c ηc (th consumr quris mor oftn bcaus sh has to pay lss). Th compnsation for a rqustd dcras in th xprt s f from c to c is thus β = (c d )η c (c d )η c. Th ovrall wlfar pr agnt in this cas incrass by V c Vc, whr V c and Vc ar th xpctd valu of sarchrs according to Equation 6-8, whn th xprt uss a f c and c rspctivly, at a cost β to th markt dsignr. Sinc th xprt is fully compnsatd for hr loss du to th dcras in hr f, th chang in th ovrall social wlfar is V c Vc β. Undr th nw pricing schm c, and givn th subsidy β, th social wlfar is givn by W = V c + π β. In th following sction w illustrat how such a subsidy β can hav a positiv chang ovr th social wlfar. An intrsting spcial cas to considr is whn d =. W can think of this cas as digital srvics, analogous to digital goods lik music MP3s producing an xtra on of ths has zro marginal cost. Similarly, producing an xtra lctronic history of a car, lik a Carfax rport, can b considrd to hav zro marginal cost. In this cas, thr is no socital cost to highr utilization of th xprt s srvics, so subsidy is wlfar improving right up to making th srvic fr. Ths ar th cass whr it could mak sns for th markt dsignr or govrnmnt to tak ovr offring th srvic thmslvs, and making it fr, potntially lvraging th incrasd wlfar of consumrs by attracting mor consumrs to thir markt, or incrasing thir fs. 5. A SPECIFIC EXAMPLE In this sction w illustrat th thortical analysis givn in th formr sction for a particular plausibl distribution of signals and valus. This cas illustrats th gnral structur of th solutions of th modl and dmonstrats how intrvntions by th markt dsignr can incras social wlfar. W considr a cas whr th signal is an uppr bound on th tru valu. Going back to th usd car xampl, sllrs and dalrs offring cars for sal usually mak cosmtic improvmnts to th cars in qustion, and procd to advrtis thm in th most appaling mannr possibl, hiding dfcts using tmporary fixs. Spcifically, w assum signals s ar

6 1.9.8 Signal(s) vs Sarch Cost(c s ) for c =.5 t l t u V(sarchr s utility) vs c s (sarch cost) c =.3 c =.6 c =.12 No Exprt.6 signal >.7 V > c s > c s > (a) Signal thrshold vs c s (b) Variation of agnt utility w.r.t c s and c Figur 2: Effct of c s on th signal thrsholds (t l,t u) and agnt utility V uniformly distributd on [, 1], and th conditional dnsity of tru valus is linar on [, s]. Thus { 1 if < s < 1 for y s f s(s) = f v(y s) = { 2y s 2 othrwis Othrwis W can substitut in ths distributions in Equations 6 through 8 and simplify. From Equation 6: V = c s + V t l c (t u t l ) + V 3 (t u t l ) 3t ut l V = 2t l 3 + V 3 c (from Equation 7) c = V 3t 2 l (V y)f v(y t u) dy = V 3 3t 2 u + 1 t2 l 3 (from Equation 8) W can find fasibl solutions of this systm for diffrnt paramtr valus, as long as th condition t l < t u holds. Othrwis, whn c is high nough that qurying nvr maks sns, a singl thrshold srvs as th optimal stratgy, as in th cas with no xprt. In th lattr cas, w obtain th optimal rsrvation valu to b usd by th sarchr from Equation 3, yilding t = 1 3c s. Th othr thing to not hr is that Equation 8 abov is for th cas whn th support on signal s is unboundd. Whn thr is an uppr limit on s i. s m for som m (as is th cas hr, whr signals ar boundd in [, 1]), onc t u rachs m (w nvr buy without qurying), Equation 8 dos not hold. Now th systm rjcts if th signal is blow t l or quris if it is abov. Figur 2(a) illustrats how th rsrvation valus t l and t u chang as a function of c s for c =.5. Th vrtical axis is th intrval of signals. As can b sn from th graph, for vry small sarch cost (c s) valus, th sarchr nvr trminats sarch without qurying th xprt. 1 Du to th low sarch cost th sarchr is bttr off only qurying th xprt whn a high signal is rcivd. Th xprt option is prfrrd ovr accpting without qurying th xprt for thos high signals, bcaus if a low valu is rcivd from th xprt thn th cost of finding a nw opportunity with a high signal is low. As th sarch cost c s incrass, thr is som 1 Whn sarch costs ar th problm is ill-dfind. Th first point on th graph shows an xtrmly low, but nonzro sarch cost. In this cas t u = 1 and t l is almost 1, but not xactly, and th xprt is again always qurid. π > Profit of Exprt vs Cost pr qury for c s =.1 d = d =.25 d = Cost pr qury(c ) > Figur 3: Exprt s profit as a function of c and d for c s =.1. bhavior that is not immdiatly intuitiv. Th rsrvation valus t l and t u bcom closr to ach othr until coinciding at c s =.8, at which point th xprt is nvr qurid anymor. Th rason for this is that th ovrall valu of continuing sarch gos down significantly as c s incrass, thrfor th cost of qurying th xprt bcoms a mor significant fraction of th total cost, making it comparativly lss dsirabl. This is a good xampl of th additional complxity of analyzing a systm with an xprt, bcaus in th static sns th cost of consulting th xprt dos not chang, so th fact that th xprt should b consultd lss and lss frquntly is countr-intuitiv. Figur 2(b) illustrats th chang in th sarchr s wlfar as a function of th sarch cost, c s, for diffrnt valus of th srvic f, c, chargd by th xprt. As xpctd, th sarchr s wlfar is bttr with th xprt option than without, and th smallr th f chargd by th xprt, th bttr th sarchr s wlfar. Expctd numbr of quris. W can find th xpctd numbr of quris in this cas by using our knowldg of th uniform distribution and th nois distribution in Equations 11-15, yilding A = V 2 ( 1 t l 1 t u ); B = t l ; C = (1 t u); D = t u t l V 2 ( 1 t l 1 t u ) which giv th final xprssions: η c = t l t u(t u t l ) t ut 2 l t lv 2 t ut l + t ; 1 uv 2 ηcs = 1 t l V 2 ( 1 t l 1 t u )

7 Th monopolist xprt s optimal stratgy. Using th abov drivations, it is now asy to calculat numrically th valu of c that maximizs π, trading off dcrasing numbr of quris η and incrasing rvnu pr qury c. Figur 3 shows xampls of th graph of xpctd profit for th xprt as a function of th xprt s f, c, for diffrnt valus of d, th marginal cost to th xprt of producing an xtra xprt rport, for c s =.1. Subsidizing th xprt. As discussd abov, th markt dsignr or th govrnmnt can guarant th rduction of th xprt s charg from c to c, kping π constant, by paying a pr-consumr subsidy β to th xprt. Figur 4 shows th improvmnt in social wlfar, dnotd δ(w ), as a function of th subsidy paid to th xprt, β, for various d valus (whr c s =.1). From th graphs, w do indd find that subsidization can lad to substantial incrass in social wlfar, vn whn thr is a significant marginal cost of producing an xprt rport. Whil this could b from a rduction in sarch and qury costs or an incras in th xpctd valu of th opportunity finally takn, th data in Tabl 1 indicats that th lattr xplanation is th dominant factor in this cas. It is also worth noting that social wlfar is maximizd at th point whr th sarchr pays xactly d pr qury, thus fully intrnalizing th cost to th xprt of producing th xtra rport. If th sarchr had to pay lss, it would lad to infficint ovrconsumption of xprt srvics, whras if sh had to pay mor, th xpctd dclin in th valu sh rcivs from participating in th sarch procss would outwigh th savings to th markt dsignr or govrnmnt from having to pay lss subsidy. 6. RELATED WORK Th autonomous agnts litratur has oftn considrd th problm of sarch which incurs a cost [2, 9, 1]. Th undrlying foundation for such analysis is sarch thory [4, 15], and in particular, its on-sidd branch which considrs an individual squntially rviwing diffrnt opportunitis from which sh can choos only on. Th sarch incurs a cost and th individual is intrstd in minimizing xpctd cost or maximizing xpctd utility ([13, 7, 16], and rfrncs thrin). To th bst of our knowldg, non of th onsidd sarch litratur in ithr sarch thory or multi-agnt systms, has considrd th rsulting markt dynamics whn obsrvations ar not accurat and mor accurat information can b purchasd from a slf-intrstd agnt. Rlaxation of th prfct signals assumption is typically found in modls of two-sidd sarch [1], including marriag or dating markts [3] and markts with intrviwing [11]. Th litratur has not to this point focusd on th dcision problms facd by slf-intrstd knowldg brokrs, or how thir prsnc affcts th markt. In trms of markt intrvntions, th two-sidd sarch litratur has considrd th impact of sarch frictions on labor markts (th 21 Nobl Priz in Economics was awardd for this work [15, 4]). On classic rgulatory intrvntion in ths modls is th introduction of a minimum wag, which can b shown to b wlfar incrasing in many contxts [8], but w ar unawar on any work on subsidizing providrs of xprt knowldg, as w discuss hr. 7. DISCUSSION AND CONCLUSIONS Th powr of modling markts using sarch thory is wll stablishd in th litratur on conomics and social scinc [12; 1, intr alia]. It has ld to brakthroughs in undrstanding many domains, ranging from basic bilatral trad [17] to labor markts [15]. Whil knowldg has always bn an conomically valuabl commodity, its rol continus to grow in th Intrnt ag. Th ubiquity of lctronic rcords and communications mans thr is an incrasing rol for knowldg brokrs in today s marktplacs. For xampl, it is now fasibl for agncis lik Carfax to collct th availabl rcords of vry rcordd accidnt, insuranc claim, oil chang, inspction, and so on for vry car. Th prsnc of such knowldg brokrs ncssitat that w tak thm into account in modling th sarch procss of consumrs. This papr taks th first stp in this dirction. W introduc a sarch modl in which agnts rciv noisy signals of th tru valu of an objct, and can pay an xprt to rval mor information. W show that, for a natural and gnral class of distributions, th sarchrs optimal stratgy is a doubl rsrvation stratgy, whr sh maintains two thrsholds, an uppr and a lowr on. Whn sh rcivs a signal blow hr lowr thrshold, sh rjcts it immdiatly. Similarly, whn sh rcivs a signal abov hr uppr thrshold, sh accpts it immdiatly. Only whn th signal is btwn th thrsholds dos sh consult th xprt, dtrmining whthr to continu sarching or accpt th offr basd on th information rvald by th xprt. In such modls, thr is scop for an authority lik a markt dsignr or rgulator to improv social wlfar by subsidizing th cost of qurying th xprt. Th bnfit to th sarchr of having lss friction in th procss could potntially mor than offst th cost to th authority. Th downsid would b that if th authority providd too much subsidy, this could lad to infficint ovrconsumption of costly (to produc) xprt srvics. By solving th modl for a natural combination of th distribution of signals and th conditional distribution of th tru valu givn th signal, w can analyz such qustions mor spcifically. W show that in our xampl, subsidis can in fact b wlfar-nhancing, and, in fact, social wlfar is maximizd whn th sarchr has to pay xactly th marginal production cost of xprt srvics. Both th modl and our rsults ar significant for dsignrs of markts in which consumrs will sarch and th nd for xprt srvics will aris naturally (lik an Intrnt marktplac for usd cars), bcaus by nhancing social wlfar, th markt dsignr can tak markt shar away from comptitors, or prhaps charg highr commissions, bcaus it is offring a bttr marktplac for consumrs. Thr ar svral dirctions for futur rsarch, from both th xprt s prspctiv and th markt-dsignr s. An intrsting problm for th monopolist xprt is th optimal pricing of bundls of quris, whr agnts must purchas a bundl, instad of individual rports. Mor ralistic modling of startup costs and hnc th avrag supply curv of xprt srvics (instad of th marginal cost considrd hr) may also xplain a richr rang of bhaviors. Th xistnc of th xprt has ramifications byond on-sidd sarch, our focus in this papr. For xampl, in two-sidd sarch markts lik labor markts, thr may b diffrnt typs of xprts: thos who conduct background chcks, for xampl, or providrs who run indpndnt tsting srvics to vt potntial mploys. What ar thir incntivs, and

8 Without Subsidy With Subsidy d c η c c c sη s Worth V W subsidy c η c c c sη s Worth V W Tabl 1: Th diffrnt componnts of social wlfar with and without subsidy for c s =.1. Worth is th xpctd valu of th opportunity vntually pickd. Initially th dcras in qury cost contributs mor to th incras in social wlfar, but as d incrass, this contribution bcoms lss significant. Not that th first two columns in th cas without subsidy ar similar bcaus th profit-maximizing c is th sam and th sarchr s cost dpnds only on valu of slctd c, not d..25 Incras in Social wlfar vs Subsidy for c s =.1 and d = 6 x 1 3 Incras in Social wlfar vs Subsidy for c s =.1 and d =.25.1 Incras in Social wlfar vs Subsidy for c s =.1 and d = Incras in social wlfar >.15.1 Incras in social wlfar > Incras in social wlfar > Subsidy(β) > Subsidy(β) > Subsidy(β) > for d = for d =.25 for d =.5 Figur 4: Incras in social wlfar vs subsidy. Whn thr is no marginal cost (d = ), it is bttr for th markt dsignr to mak th srvic availabl for fr but whn thr is som marginal cost involvd, thn incras in social wlfar is a concav pakd at marginal cost. how do ths affct two-sidd sarch markts? From th markt dsignr s point of viw, nw altrnativs to subsidization as a mans for improving social wlfar can b xplord,.g., inducing comptition, or provision of xprt srvics by th markt dsignr hrslf (.g., a govrnmnt taks ovr th rol of providing xprt srvics). 8. ACKNOWLEDGMENTS W ar gratful to th US-Isral BSF for supporting this rsarch undr Grant Das also acknowldgs support from an NSF CAREER award (952918), and Sarn is partially supportd by ISF grants 141/9. 9. REFERENCES [1] K. Burdtt and R. Wright. Two-sidd sarch with nontransfrabl utility. Rviw of Economic Dynamics, 1:22 245, [2] S. Choi and J. Liu. Optimal tim-constraind trading stratgis for autonomous agnts. In Proc. MAMA, 2. [3] S. Das and E. Kamnica. Two-sidd bandits and th dating markt. In Proc. IJCAI, 25. [4] P. Diamond. Aggrgat dmand managmnt in sarch quilibrium. Th Journal of Political Economy, 9(5): , [5] D. Fudnbrg and J. Tirol. Gam Thory. MIT Prss, [6] J. Gilbrt and F. Mostllr. Rcognizing th maximum of a squnc. Journal of th Amrican Statistical Association, 61:35 73, [7] A. Grosfld-Nir, D. Sarn, and I. Spiglr. Modling th sarch for th last costly opportunity. Europan Journal of Oprational Rsarch, 197(2): , 29. [8] L. Ho. Wag subsidis as a labour markt policy tool. Policy Scincs, 33(1):89 1, 2. [9] J. Kphart and A. Grnwald. Shopbot conomics. JAAMAS, 5(3): , 22. [1] J. O. Kphart, J. E. Hanson, and A. R. Grnwald. Dynamic pricing by softwar agnts. Computr Ntworks, 32: , 2. [11] R. L and M. Schwarz. Intrviwing in two-sidd matching markts. NBER Working Papr, 29. [12] S. Lippman and J. McCall. Th conomics of job sarch: A survy. Economic Inquiry, 14: , [13] J. McMillan and M. Rothschild. Sarch. In R. Aumann and S. Hart, ditors, Handbook of Gam Thory with Economic Applications, pags [14] P. Milgrom. Good nws and bad nws: Rprsntation thorms and applications. Th Bll Journal of Economics, pags , [15] D. Mortnsn and C. Pissarids. Nw dvlopmnts in modls of sarch in th labor markt. Handbook of labor conomics, 3: , [16] M. Rothschild. Sarching for th lowst pric whn th distribution of prics is unknown. Journal of Political Economy, 82: , [17] A. Rubinstin and A. Wolinsky. Middlmn. Th Quartrly Journal of Economics, 12(3): , [18] M. Witzman. Optimal sarch for th bst altrnativ. Economtrica: Journal of th Economtric Socity, 47(3): , [19] R. Wright. Job sarch and cyclical unmploymnt. Th Journal of Political Economy, 94(1):38 55, 1986.

Adverse Selection and Moral Hazard in a Model With 2 States of the World

Adverse Selection and Moral Hazard in a Model With 2 States of the World Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,

More information

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13)

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13) con 37: Answr Ky for Problm St (Chaptr 2-3) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc

More information

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book.

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book. Rsourc Allocation Abstract This is a small toy xampl which is wll-suitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of C-nts. Hnc, it can b rad by popl

More information

QUANTITATIVE METHODS CLASSES WEEK SEVEN

QUANTITATIVE METHODS CLASSES WEEK SEVEN QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.

More information

Question 3: How do you find the relative extrema of a function?

Question 3: How do you find the relative extrema of a function? ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating

More information

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix Non-Homognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous first-ordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach

More information

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs

More information

Performance Evaluation

Performance Evaluation Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Bay-lik rputation systms: Analysis, charactrization and insuranc mchanism

More information

Fraud, Investments and Liability Regimes in Payment. Platforms

Fraud, Investments and Liability Regimes in Payment. Platforms Fraud, Invstmnts and Liability Rgims in Paymnt Platforms Anna Crti and Mariann Vrdir y ptmbr 25, 2011 Abstract In this papr, w discuss how fraud liability rgims impact th pric structur that is chosn by

More information

Rural and Remote Broadband Access: Issues and Solutions in Australia

Rural and Remote Broadband Access: Issues and Solutions in Australia Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity

More information

Foreign Exchange Markets and Exchange Rates

Foreign Exchange Markets and Exchange Rates Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) 92.222 - Linar Algbra II - Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial

More information

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers) Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly

More information

Electronic Commerce. and. Competitive First-Degree Price Discrimination

Electronic Commerce. and. Competitive First-Degree Price Discrimination Elctronic Commrc and Comptitiv First-Dgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg

More information

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS 25 Vol. 3 () January-March, pp.37-5/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut

More information

(Analytic Formula for the European Normal Black Scholes Formula)

(Analytic Formula for the European Normal Black Scholes Formula) (Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually

More information

Asset set Liability Management for

Asset set Liability Management for KSD -larning and rfrnc products for th global financ profssional Highlights Library of 29 Courss Availabl Products Upcoming Products Rply Form Asst st Liability Managmnt for Insuranc Companis A comprhnsiv

More information

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:

More information

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 08-16-85 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt

More information

Architecture of the proposed standard

Architecture of the proposed standard Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th

More information

AP Calculus AB 2008 Scoring Guidelines

AP Calculus AB 2008 Scoring Guidelines AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.

More information

Gold versus stock investment: An econometric analysis

Gold versus stock investment: An econometric analysis Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 268-8662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag -7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin

More information

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim

More information

Lecture 3: Diffusion: Fick s first law

Lecture 3: Diffusion: Fick s first law Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th

More information

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing Uppr Bounding th Pric of Anarchy in Atomic Splittabl Slfish Routing Kamyar Khodamoradi 1, Mhrdad Mahdavi, and Mohammad Ghodsi 3 1 Sharif Univrsity of Tchnology, Thran, Iran, khodamoradi@c.sharif.du Sharif

More information

A Note on Approximating. the Normal Distribution Function

A Note on Approximating. the Normal Distribution Function Applid Mathmatical Scincs, Vol, 00, no 9, 45-49 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and

More information

Long run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange

Long run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity

More information

Theoretical aspects of investment demand for gold

Theoretical aspects of investment demand for gold Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is

More information

Remember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D

Remember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D 24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd

More information

Free ACA SOLUTION (IRS 1094&1095 Reporting)

Free ACA SOLUTION (IRS 1094&1095 Reporting) Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 279-1062 ACA Srvics Transmit IRS Form 1094 -C for mployrs Print & mail IRS Form 1095-C to mploys HR Assist 360 will gnrat th 1095 s for

More information

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13 Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions

More information

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives. Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud

More information

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among

More information

Traffic Flow Analysis (2)

Traffic Flow Analysis (2) Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,

More information

Planning and Managing Copper Cable Maintenance through Cost- Benefit Modeling

Planning and Managing Copper Cable Maintenance through Cost- Benefit Modeling Planning and Managing Coppr Cabl Maintnanc through Cost- Bnfit Modling Jason W. Rup U S WEST Advancd Tchnologis Bouldr Ky Words: Maintnanc, Managmnt Stratgy, Rhabilitation, Cost-bnfit Analysis, Rliability

More information

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 50-54 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin

More information

Parallel and Distributed Programming. Performance Metrics

Parallel and Distributed Programming. Performance Metrics Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:

More information

STATEMENT OF INSOLVENCY PRACTICE 3.2

STATEMENT OF INSOLVENCY PRACTICE 3.2 STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr

More information

Category 7: Employee Commuting

Category 7: Employee Commuting 7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil

More information

The Normal Distribution: A derivation from basic principles

The Normal Distribution: A derivation from basic principles Th Normal Distribution: A drivation from basic principls Introduction Dan Tagu Th North Carolina School of Scinc and Mathmatics Studnts in lmntary calculus, statistics, and finit mathmatics classs oftn

More information

IMES DISCUSSION PAPER SERIES

IMES DISCUSSION PAPER SERIES IMES DISCUSSIN PAPER SERIES Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I, Akira TANI, and Toyoichirou SHIRTA Discussion Papr No. 003-E-13

More information

Defining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind

Defining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind Dfining Rtirmnt Succss for Dfind Contribution Plan Sponsors: Bgin with th End in Mind David Blanchtt, CFA, CFP, AIFA Had of Rtirmnt Rsarch Morningstar Invstmnt Managmnt david.blanchtt@morningstar.com Nathan

More information

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* Rostov-on-Don. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

Sci.Int.(Lahore),26(1),131-138,2014 ISSN 1013-5316; CODEN: SINTE 8 131

Sci.Int.(Lahore),26(1),131-138,2014 ISSN 1013-5316; CODEN: SINTE 8 131 Sci.Int.(Lahor),26(1),131-138,214 ISSN 113-5316; CODEN: SINTE 8 131 REQUIREMENT CHANGE MANAGEMENT IN AGILE OFFSHORE DEVELOPMENT (RCMAOD) 1 Suhail Kazi, 2 Muhammad Salman Bashir, 3 Muhammad Munwar Iqbal,

More information

Use a high-level conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects

Use a high-level conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects Chaptr 3: Entity Rlationship Modl Databas Dsign Procss Us a high-lvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End

More information

Deer: Predation or Starvation

Deer: Predation or Starvation : Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,

More information

union scholars program APPLICATION DEADLINE: FEBRUARY 28 YOU CAN CHANGE THE WORLD... AND EARN MONEY FOR COLLEGE AT THE SAME TIME!

union scholars program APPLICATION DEADLINE: FEBRUARY 28 YOU CAN CHANGE THE WORLD... AND EARN MONEY FOR COLLEGE AT THE SAME TIME! union scholars YOU CAN CHANGE THE WORLD... program AND EARN MONEY FOR COLLEGE AT THE SAME TIME! AFSCME Unitd Ngro Collg Fund Harvard Univrsity Labor and Worklif Program APPLICATION DEADLINE: FEBRUARY 28

More information

7 Timetable test 1 The Combing Chart

7 Timetable test 1 The Combing Chart 7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing

More information

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means Qian t al. Journal of Inqualitis and Applications (015) 015:1 DOI 10.1186/s1660-015-0741-1 R E S E A R C H Opn Accss Sharp bounds for Sándor man in trms of arithmtic, gomtric and harmonic mans Wi-Mao Qian

More information

Budget Optimization in Search-Based Advertising Auctions

Budget Optimization in Search-Based Advertising Auctions Budgt Optimization in Sarch-Basd Advrtising Auctions ABSTRACT Jon Fldman Googl, Inc. Nw York, NY jonfld@googl.com Martin Pál Googl, Inc. Nw York, NY mpal@googl.com Intrnt sarch companis sll advrtismnt

More information

A Theoretical Model of Public Response to the Homeland Security Advisory System

A Theoretical Model of Public Response to the Homeland Security Advisory System A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial

More information

C H A P T E R 1 Writing Reports with SAS

C H A P T E R 1 Writing Reports with SAS C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd

More information

REPORT' Meeting Date: April 19,201 2 Audit Committee

REPORT' Meeting Date: April 19,201 2 Audit Committee REPORT' Mting Dat: April 19,201 2 Audit Committ For Information DATE: March 21,2012 REPORT TITLE: FROM: Paul Wallis, CMA, CIA, CISA, Dirctor, Intrnal Audit OBJECTIVE To inform Audit Committ of th rsults

More information

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000 hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails

More information

New Basis Functions. Section 8. Complex Fourier Series

New Basis Functions. Section 8. Complex Fourier Series Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ral-valud Fourir sris is xplaind and formula ar givn for convrting

More information

Basis risk. When speaking about forward or futures contracts, basis risk is the market

Basis risk. When speaking about forward or futures contracts, basis risk is the market Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also

More information

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole Th intrnational Intrnt sit of th goviticultur MCC systm L sit Intrnt intrnational du systèm CCM géoviticol Flávio BELLO FIALHO 1 and Jorg TONIETTO 1 1 Rsarchr, Embrapa Uva Vinho, Caixa Postal 130, 95700-000

More information

Policies for Simultaneous Estimation and Optimization

Policies for Simultaneous Estimation and Optimization Policis for Simultanous Estimation and Optimization Migul Sousa Lobo Stphn Boyd Abstract Policis for th joint idntification and control of uncrtain systms ar prsntd h discussion focuss on th cas of a multipl

More information

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY 1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically

More information

Analyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms

Analyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas

More information

TIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.

TIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1. Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M

More information

Constraint-Based Analysis of Gene Deletion in a Metabolic Network

Constraint-Based Analysis of Gene Deletion in a Metabolic Network Constraint-Basd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFG-Rsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany

More information

SOFTWARE ENGINEERING AND APPLIED CRYPTOGRAPHY IN CLOUD COMPUTING AND BIG DATA

SOFTWARE ENGINEERING AND APPLIED CRYPTOGRAPHY IN CLOUD COMPUTING AND BIG DATA Intrnational Journal on Tchnical and Physical Problms of Enginring (IJTPE) Publishd by Intrnational Organization of IOTPE ISSN 077-358 IJTPE Journal www.iotp.com ijtp@iotp.com Sptmbr 015 Issu 4 Volum 7

More information

Online Price Competition within and between Heterogeneous Retailer Groups

Online Price Competition within and between Heterogeneous Retailer Groups Onlin Pric Comptition within and btwn Htrognous Rtailr Groups Cnk Kocas Dpartmnt of Markting and Supply Chain Managmnt, Michigan Stat Univrsity kocas@msu.du Abstract This study prsnts a modl of pric comptition

More information

Economic Insecurity, Individual Behavior and Social Policy

Economic Insecurity, Individual Behavior and Social Policy Economic Inscurity, Individual Bhavior and Social Policy By Indrmit S. Gill igill@worldbank.org and Nadm Ilahi nilahi@worldbank.org Th World Bank Washington, DC 20433 First Draft: March 27, 2000 Papr writtn

More information

Global Sourcing: lessons from lean companies to improve supply chain performances

Global Sourcing: lessons from lean companies to improve supply chain performances 3 rd Intrnational Confrnc on Industrial Enginring and Industrial Managmnt XIII Congrso d Ingniría d Organización Barclona-Trrassa, Sptmbr 2nd-4th 2009 Global Sourcing: lssons from lan companis to improv

More information

The Constrained Ski-Rental Problem and its Application to Online Cloud Cost Optimization

The Constrained Ski-Rental Problem and its Application to Online Cloud Cost Optimization 3 Procdings IEEE INFOCOM Th Constraind Ski-Rntal Problm and its Application to Onlin Cloud Cost Optimization Ali Khanafr, Murali Kodialam, and Krishna P. N. Puttaswam Coordinatd Scinc Laborator, Univrsit

More information

In the first years of the millennium, Americans flocked to Paris to enjoy French

In the first years of the millennium, Americans flocked to Paris to enjoy French 14 chaptr Exchang Rats and th Forign Exchang Markt: An Asst Approach 320 In th first yars of th millnnium, Amricans flockd to Paris to njoy Frnch cuisin whil shopping for dsignr clothing and othr spcialtis.

More information

Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis ch03.qxd 9/7/04 4:06 PM Pag 86 CHAPTER Cost-Volum-Profit Analysis In Brif Managrs nd to stimat futur rvnus, costs, and profits to hlp thm plan and monitor oprations. Thy us cost-volum-profit (CVP) analysis

More information

A Project Management framework for Software Implementation Planning and Management

A Project Management framework for Software Implementation Planning and Management PPM02 A Projct Managmnt framwork for Softwar Implmntation Planning and Managmnt Kith Lancastr Lancastr Stratgis Kith.Lancastr@LancastrStratgis.com Th goal of introducing nw tchnologis into your company

More information

Entity-Relationship Model

Entity-Relationship Model Entity-Rlationship Modl Kuang-hua Chn Dpartmnt of Library and Information Scinc National Taiwan Univrsity A Company Databas Kps track of a company s mploys, dpartmnts and projcts Aftr th rquirmnts collction

More information

GOAL SETTING AND PERSONAL MISSION STATEMENT

GOAL SETTING AND PERSONAL MISSION STATEMENT Prsonal Dvlopmnt Track Sction 4 GOAL SETTING AND PERSONAL MISSION STATEMENT Ky Points 1 Dfining a Vision 2 Writing a Prsonal Mission Statmnt 3 Writing SMART Goals to Support a Vision and Mission If you

More information

ME 612 Metal Forming and Theory of Plasticity. 6. Strain

ME 612 Metal Forming and Theory of Plasticity. 6. Strain Mtal Forming and Thory of Plasticity -mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.

More information

the so-called KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through

the so-called KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through Liquidity and Information-Basd Trading on th Ordr Drivn Capital Markt: Th Cas of th Pragu tock Exchang Libor 1ÀPH³HN Cntr for Economic Rsarch and Graduat Education, Charls Univrsity and Th Economic Institut

More information

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs

More information

Increasing Net Debt as a percentage of Average Equalized ValuaOon

Increasing Net Debt as a percentage of Average Equalized ValuaOon City of Orang Township Warning Trnd: Incrasing Nt Dbt as a prcntag of avrag qualizd valuation Nt Dbt 3 yr. Avg. qualizd Valuation Incrasing Nt Dbt as a prcntag of Avrag Equalizd ValuaOon rc 1.20% 1.00%

More information

Factorials! Stirling s formula

Factorials! Stirling s formula Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical

More information

Version 1.0. General Certificate of Education (A-level) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final.

Version 1.0. General Certificate of Education (A-level) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final. Vrsion.0 Gnral Crtificat of Education (A-lvl) January 0 Mathmatics MPC (Spcification 660) Pur Cor Final Mark Schm Mark schms ar prpard by th Principal Eaminr and considrd, togthr with th rlvant qustions,

More information

IBM Healthcare Home Care Monitoring

IBM Healthcare Home Care Monitoring IBM Halthcar Hom Car Monitoring Sptmbr 30th, 2015 by Sal P. Causi, P. Eng. IBM Halthcar Businss Dvlopmnt Excutiv scausi@ca.ibm.com IBM Canada Cloud Computing Tigr Tam Homcar by dfinition 1. With a gnsis

More information

Important Information Call Through... 8 Internet Telephony... 6 two PBX systems... 10 Internet Calls... 3 Internet Telephony... 2

Important Information Call Through... 8 Internet Telephony... 6 two PBX systems... 10 Internet Calls... 3 Internet Telephony... 2 Installation and Opration Intrnt Tlphony Adaptr Aurswald Box Indx C I R 884264 03 02/05 Call Duration, maximum...10 Call Through...7 Call Transportation...7 Calls Call Through...7 Intrnt Tlphony...3 two

More information

Production Costing (Chapter 8 of W&W)

Production Costing (Chapter 8 of W&W) Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary

More information

B-285141. April 21, 2000. The Honorable Charles B. Rangel Ranking Minority Member Committee on Ways and Means House of Representatives

B-285141. April 21, 2000. The Honorable Charles B. Rangel Ranking Minority Member Committee on Ways and Means House of Representatives Unit Stats Gnral Accounting Offic Washington, DC 20548 Halth, Eucation, an Human Srvics Division B-285141 April 21, 2000 Th Honorabl Charls B. Rangl Ranking Minority Mmbr Committ on Ways an Mans Hous of

More information

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos

More information

June 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8

June 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8 Jun 22 Enpris Rnt Author: Documnt Vrsion: Product: Product Vrsion: SAP Vrsion: Enpris Enpris Rnt 88 88 Enpris Rnt 22 Enpris Solutions All rights rsrvd No parts of this work may b rproducd in any form or

More information

User-Perceived Quality of Service in Hybrid Broadcast and Telecommunication Networks

User-Perceived Quality of Service in Hybrid Broadcast and Telecommunication Networks Usr-Prcivd Quality of Srvic in Hybrid Broadcast and Tlcommunication Ntworks Michal Galtzka Fraunhofr Institut for Intgratd Circuits Branch Lab Dsign Automation, Drsdn, Grmany Michal.Galtzka@as.iis.fhg.d

More information

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd

More information

Statistical Machine Translation

Statistical Machine Translation Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm

More information

Lecture 20: Emitter Follower and Differential Amplifiers

Lecture 20: Emitter Follower and Differential Amplifiers Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.

More information

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison Contnts Tchnology Nwly Dvlopd Cllo Tchnology Cllo Tchnology : Improvd Absorption of Light Doubl-sidd Cll Structur Cllo Tchnology : Lss Powr Gnration Loss Extrmly Low LID Clls 3 3 4 4 4 Advantag Installation

More information

Incomplete 2-Port Vector Network Analyzer Calibration Methods

Incomplete 2-Port Vector Network Analyzer Calibration Methods Incomplt -Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar

More information

Development of Financial Management Reporting in MPLS

Development of Financial Management Reporting in MPLS 1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr

More information

Category 1: Purchased Goods and Services

Category 1: Purchased Goods and Services 1 Catgory 1: Purchasd Goods and Srvics Catgory dscription T his catgory includs all upstram (i.., cradl-to-gat) missions from th production of products purchasd or acquird by th rporting company in th

More information

The price of liquidity in constant leverage strategies. Marcos Escobar, Andreas Kiechle, Luis Seco and Rudi Zagst

The price of liquidity in constant leverage strategies. Marcos Escobar, Andreas Kiechle, Luis Seco and Rudi Zagst RACSAM Rv. R. Acad. Cin. Sri A. Mat. VO. 103 2, 2009, pp. 373 385 Matmática Aplicada / Applid Mathmatics Th pric of liquidity in constant lvrag stratgis Marcos Escobar, Andras Kichl, uis Sco and Rudi Zagst

More information

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore Intrnational Journal of mrging Tchnology and dvancd nginring Wbsit: www.ijta.com (ISSN 2250-2459, Volum 2, Issu 4, pril 2012) n road outlin of Rdundant rray of Inxpnsiv isks Shaifali Shrivastava 1 partmnt

More information

Category 11: Use of Sold Products

Category 11: Use of Sold Products 11 Catgory 11: Us of Sold Products Catgory dscription T his catgory includs missions from th us of goods and srvics sold by th rporting company in th rporting yar. A rporting company s scop 3 missions

More information

Cisco Data Virtualization

Cisco Data Virtualization Cisco Data Virtualization Big Data Eco-systm Discussion with Bloor Group Bob Ev, David Bsmr July 2014 Cisco Data Virtualization Backgroundr Cisco Data Virtualization is agil data intgration softwar that

More information

A Multi-Heuristic GA for Schedule Repair in Precast Plant Production

A Multi-Heuristic GA for Schedule Repair in Precast Plant Production From: ICAPS-03 Procdings. Copyright 2003, AAAI (www.aaai.org). All rights rsrvd. A Multi-Huristic GA for Schdul Rpair in Prcast Plant Production Wng-Tat Chan* and Tan Hng W** *Associat Profssor, Dpartmnt

More information

Essays on Adverse Selection and Moral Hazard in Insurance Market

Essays on Adverse Selection and Moral Hazard in Insurance Market Gorgia Stat Univrsity ScholarWorks @ Gorgia Stat Univrsity Risk Managmnt and Insuranc Dissrtations Dpartmnt of Risk Managmnt and Insuranc 8--00 Essays on Advrs Slction and Moral Hazard in Insuranc Markt

More information

1 Walrasian Equilibria and Market E ciency

1 Walrasian Equilibria and Market E ciency 1 Walrasian Equilibria and Markt E cincy Rading in Txtbook: Chaptr 3 in Stiglitz. 1.1 Motivation Whn thinking about th rol of govrnmnt w hav to considr a numbr of rathr fundamntal qustions, such as: What

More information