Peer-to-Peer Tangible Goods Rental

Transcription

1 Peer-to-Peer Tangble Goods Rental James A. Hll and Mchael P. Wellman Unversty of Mchgan, Computer Scence & Engneerng, 2260 Hayward St, Ann Arbor, MI , USA Abstract. We present a game-theoretc model of onlne tangble prvate goods rental. Rental mechansms adherng to ths model are classfed accordng to whether ther prncpals and transfer paths are centralzed or peer-to-peer. A key ssue n all cases s provdng ncentves for partcpants to accurately report on qualty of the rented good. Our man contrbuton s a novel mechansm for the stuaton n whch the prncpal s ndependent of the owners of goods avalable n the market and n whch goods are transferred drectly between renters. We show that t s possble to set mechansm parameters payments and penalty functons so that truthful reportng of the qualty of goods s a Nash equlbrum. Keywords: Peer-to-Peer Rental, E-Commerce, Collaboratve Consumpton, Mechansm Desgn 1 Introducton Onlne tangble prvate goods rental s an emergng market-based approach to sharng goods among strangers. By provdng a medum through whch nformaton may be stored and accessed globally, the Internet has greatly extended the feasblty of such markets. Rental enables goods owners to obtan revenue from goods that would otherwse be underutlzed, whle enablng renters to obtan utlty from goods to whch they may not otherwse have access. Commercal servces for onlne tangble goods rental have prolferated n recent years. The clamed benefts of rental are both ncreased utlty for market partcpants and a reducton of negatve envronmental externaltes [Botsman and Rogers, 2010]. ZpCar ( a renter of automobles for bref local usage wth 270, 000 users as of 2009 [Lawson, 2011], boasts a fleet sze of 9, 000 vehcles, and clams each vehcle obvates the need for 15 personally owned vehcles ( Zlok ( s a leadng rental market of many types of tangble goods, growng at a rate of 25% per year snce 2007 [Botsman and Rogers, 2010]. Includng offlne markets, U.S. consumer rental servces ncreased 27% between 1999 and 2007 to $4.7 bllon [Lawson, 2011]. Despte beng a growng economc sector, mechansms for tangble prvate goods rental have not to our knowledge been prevously studed from a game-theoretc perspectve. Market mechansms vary along two dmensons: the prncpal and the transfer path of goods. Examples of markets n ndustry that vary along these dmensons

2 2 James A. Hll, Mchael P. Wellman are provded n 3. The prncpal sets the mechansm and medates the market. The transfer path refers to the re that a good takes to move from one renter to the next. We present a framework for tangble prvate goods rental, wthn whch mechansms that vary along these dmensons can be modeled and analyzed. Our man contrbuton s a novel mechansm n whch the prncpal s ndependent of the owners of goods avalable n the market and goods are transferred drectly between renters. 2 Related Work As commercal servces for onlne tangble goods rental have emerged only recently, t s not surprsng that t has yet to receve much attenton n the research lterature. Some research has addressed the general socal-psychologcal motvatons for non-ownershp consumpton [Lawson, 2011, Lamberton and Rose, 2012, Belk, 2010, Durgee and O Connor, 1995], and n partcular on socal mechansms for sharng tangble goods [Benkler, 2004]. To our knowledge, tangble goods rental mechansms have not prevously been examned from a game-theoretc perspectve. In foundatonal work on the relatonshp between qualty and uncertanty n markets, Akerlof [1970] found that trust s a precondton for tradng goods wth uncertan qualty, such as used automobles. Rental can be reformulated as two transactons n whch qualty nformaton s asymmetrcal, and the dfference n purchase prce and sale prce equals the rental prce. For a rental market to succeed, renters must trust that the qualty of the good they are to rent s as descrbed. Sharng and rentng are two soluton concepts whch seek an effcent utlzaton of goods. Whereas sharng reles upon socal mechansms, rentng reles upon market mechansms. The focus of some sharng research consders the poolng and shared consumpton of prvate goods [Lamberton and Rose, 2012, Belk, 2010], a mechansm whch treats prvate goods as common wthn a group of agents. Such sharng arrangements may be susceptble to the Tragedy of the Commons [Hardn, 1968], n whch each agent s ratonal best response s to use, and potentally deplete, the entre pool themselves. The model n ths paper dffers n that the good s modeled as a perfectly excludable prvate good, used by a sngle agent at any one tme. Belk [2010] descrbes the sharng of jont possessons as carryng socally enforced responsbltes to not cause damage, to not overuse, and to clean up after the use of goods. The desgn goal of rental mechansms s a market-based enforcement of the same responsbltes. Benkler [2004] conjectures that some reasons socal-based sharng mechansms are more prevalent than market-based sharng mechansms are lower transacton costs, better nformaton, and stronger motvatons for owners. We smlarly observe from the model n ths paper the need to mnmze transacton costs and elct truthful reports from market partcpants n order to maxmze socal welfare.

3 3 Rental Mechansm Classes Peer-to-Peer Tangble Goods Rental 3 We classfy mechansms along two dmensons: whether the prncpal s also the owner of goods avalable n the market (central f so, peer-to-peer otherwse), and whether goods are transferred to the owner between renters (central f so, peer-to-peer otherwse). Fgure 1 presents a bref summary of the four onlne tangble goods rental mechansm classes. Rental Transfer Central Peerto-Peer Central Goods owner medates the market. Goods are transferred between renters by way of the owner. Goods owner medates the market. Goods are transferred drectly between renters. Peer-to-Peer Market medator s a thrd party to the transacton. Goods are transferred between renters by way of the owner. Market medator s a thrd party to the transacton. Goods are transferred drectly between renters. Fg. 1. Bref descrpton of each of the four mechansm classes. The frst mechansm class s central rental, central transfer, n whch renters nteract drectly wth the owner durng every stage of the transacton. When a good s returned to the owner, t s the owner who reports the current qualty of the good. We show that the best response of the owner s to report qualty untruthfully. An example of such a market s Chegg ( whch prmarly rents textbooks. The second mechansm class s central rental, peer-to-peer transfer, n whch goods are not typcally handled by the owner between rentals, but the owner sets the mechansm and medates the market. Ths market class dffers from the prevous class n that reportng damage done to a good s the responsblty of the renter. An example of such a market s ZpCar, whch rents vehcles strategcally located near clusters of renters. A renter reserves a vehcle through ZpCar s web ste, then pcks t up from the unmontored parkng lot n whch t s located. When fnshed usng the vehcle, the renter returns t to the same parkng lot. It s the responsblty of the renter to nspect the vehcle thoroughly before usng t. If the renter fals to report damage that occurred prevous to her use of the vehcle, she becomes lable for that damage. We show that, as market medator, the owner has the opportunty to falsfy reports, and thus the ncentve propertes of such a mechansm are equvalent to the central rental, central transfer mechansm. The next mechansm class s peer-to-peer rental, central transfer. In such a mechansm, renters nteract wth a thrd-party market medator to fnd and

4 4 James A. Hll, Mchael P. Wellman reserve goods before nteractng wth the owner to obtan the goods. A beneft of ths market class over central rental mechansms s that renters here may have ntramarket recourse aganst untruthful reports by owners through the use of a reputaton mechansm, whch may ncentvze the owner to report truthfully n equlbrum. An example of such a market s Zlok, a market for rental of all types of tangble goods. The fnal mechansm class s peer-to-peer rental, peer-to-peer transfer, n whch renters nteract wth a thrd-party market medator to fnd and reserve a good before nteractng wth the prevous renter to obtan the good, removng the owner from the process wth the excepton of ntroducng the good. We were unable to fnd any commercal or pror lterature examples of such a market, thus ths appears to be a novel formulaton. 4 Model We present a general model of tangble prvate goods rental. The varous mechansm classes are dstnct desgns whch conform to ths model. Utlty derved from tangble goods s a functon of several attrbutes, one of whch s tme. Some goods, such as books, have hgh utlty untl the good s consumed, at whch pont utlty drops. Other goods, such as lawn mowers, have a utlty that cycles between hgh and low over tme. Another attrbute of tangble goods that affects utlty s qualty. As a good s used, ts qualty s degraded wth some probablty per unt of tme. Our model adopts the assumpton that qualty s monotoncally decreasng. Another smplfyng assumpton we make s that agents are able to perfectly assess a good s qualty on a commonly understood dscrete-valued scale. All market partcpants are ratonal, self-nterested, and rsk-neutral. The prncpal, m, s the desgner and medator of the mechansm. The owner o of good g may or may not also be m. Utlty for g s one-tme or cyclc. There s a stream of renters ρ 0,..., ρ,..., ρ n = P who sequentally use g. Renter ρ uses g durng tme perod. At any pont n tme, g has nteger qualty q {0,..., q max } = Q such that q max 1. At the begnnng of tme perod, g has qualty q n. At the end of tme perod, g has qualty q q n. The probablty of degradng from q n to q n one tme perod s δ q n q [0, 1]. For all q n, the constrant q q δ n q n q = 1 ensures a well-defned probablty dstrbuton. We denote by ˆq a qualty report submtted to m. The symbol ˆq desgnates a truthful report, where ˆq = q. The choce of reported qualty that results n the hghest expected utlty for the reporter s denoted ˆq. To smplfy notaton and reasonng, we assume that the renters value usng g equally. The value v q of usng a good wth qualty q n = q at the begnnng of the tme perod decreases monotoncally wth q. For calbraton, we set v 0 = 0. The cost of physcally transferrng g from one agent to another s θ t, and s borne by the recevng agent. No degradaton occurs durng transfer. The cost of processng the transfer of g s θ p, whch s meant to reflect n part the cost of

5 Peer-to-Peer Tangble Goods Rental 5 effort to assess the qualty of the good. θ p s less than θ t because processng s a step n transferrng the good. A market does not exst n solaton. Dsregardng property rghts, g can be sold by the holdng agent for an amount that decreases monotoncally wth g s qualty, c q, wth c 0 = 0. At the begnnng of the game, o has purchased g at cost c q max. Consder frst a basc mechansm n whch ρ pays some amount to o n exchange for rentng g. The payment pˆq n decreases monotoncally wth reported ncomng qualty, ˆq n, wth p 0 = 0. A goal of the mechansm s to ncentvze ρ to return g when fnshed usng t. When ρ holds g, she has the opportunty to sell t for the amount c q. When ρ returns g, she receves 0 addtonal utlty, whereas she receves c q addtonal utlty when she sells g. Because c q > 0 for q > 0 by defnton, t s mpossble to ncentvze ρ to return g wth ths basc payment mechansm. Ths s n lne wth the ntutve noton that the same mechansm for sellng goods cannot also be used to rent goods. A soluton to the return problem s to nclude a depost, by whch ρ loses d when g s not returned at the end of the tme perod. A depost ncentvzes ρ to return g when c < d. Ths s n lne wth the mechansms of observed markets. Zlok requres renters post a depost n order to rent a good, and Chegg holds monetary account nformaton n order to charge the dfference between the purchase prce and the rental prce n the event a book s not returned ( Let u o denote the utlty of the owner, and u ρ the utlty of a renter. The functons u o and u ρ may dffer between mechansms. We defne socal welfare w to be the sum of the expected utltes of all market partcpants, w = E[u o ] ρ P E[u ρ ]. Wth ndvdual ratonalty constrants ensurng that expected utlty s nonnegatve, socal welfare s proportonal to the number of renters. Thus, ncreasng the number of renters ncreases socal welfare. What prevents the number of renters from reachng nfnty s the probablstc degradaton of the qualty of g. When the probablty of degradaton s hgher, the expected lfespan of the good s lower, and thus the number of renters expected to use the good s lower. Consder the addton of a reward to the mechansm, by whch ρ receves an amount of utlty that decreases monotoncally wth the value of reported gong qualty, rˆq, wth r 0 = 0. Assumng ρ has the ablty to control her probablty of degradng q at some cost of effort, she wll respond to the reward by ncreasng the care wth whch g s handled by an amount that s a functon of effort, thus decreasng the probablty that q degrades. Socal welfare can be further ncreased by mnmzng the cost of transferrng a good between renters. Ths provdes motvaton to the peer-to-peer transfer of goods, n whch goods are transferred drectly from one renter to the next nstead of beng red through the owner, reducng the number of transfers by approxmately half.

6 6 James A. Hll, Mchael P. Wellman 5 Central Rental Mechansms In central rental mechansms, m and o are the same agent. Treatng rental as a one-shot nteracton, ths provdes o wth substantal power to manpulate the market to her beneft. Owner o reports ˆq n the central transfer mechansm, whle ρ reports ˆq n the peer-to-peer transfer mechansm. Because o s also m, o has the opportunty to falsfy reports by ρ, and thus the two mechansms may both be modeled as f o reports ˆq. Ths scenaro s represented as a two-player sequental game n whch o chooses ˆq n, ρ obtans, uses, and chooses whether to return g, then o chooses ˆq. An avalable strategy of o s to whte-wash the qualty of g. Whte-washng s a strategy commonly consdered for cleansng agent reputatons [Feldman et al., 2006]. Ths strategy s appled here to a good, whch enables o to make ndependent reports of qualty between renters of the same good. Applyng ths strategy, o s expected utlty when reportng ˆq = 0 s greater than o s expected utlty when reportng ˆq > 0 by rˆq, whch s non-negatve by defnton, so ˆq = 0 and whte-washng g s the best response by o when ρ returns g. It s n the best nterest of o to ncentvze ρ to return g, whch s accomplshed wth a depost d. Even though ρ does not expect to receve reward, the alternatve choce of losng c q d ncentvzes ρ to return g. Whereas the central rental mechansms may be functonal n that the renter wll return the good, ρ s effectvely charged based on completely degradng the good, and so rental wll not occur unless the value s exceedngly hgh. Moreover, even when rental does take place, ρ lacks any ncentve to take care n handlng g to preserve ts qualty. A more extreme result occurs when the owner reneges on the promsed return of the depost. In ths case, the best response of the renter s to sell the good nstead of returnng t, and the market breaks down n equlbrum. We emphasze that these conclusons rely on the fact that n a one-shot nteracton, the owner can act wth mpunty n whte-washng reputatons and even renegng on returnng deposts. In realty, nteractons may repeat or play publcly over tme, n whch case other forces (e.g., through external reputaton channels), not modeled here, may substantally check the owner s power. Wth such extensons, central rental may work well n practce. Thus, we consder more salent our postve results on peer-to-peer markets, where we can acheve desrable propertes even n ths smple one-shot nteracton model. 6 Peer-to-Peer Rental Mechansms Recall that peer-to-peer rental mechansms dffer from central rental mechansms n that the market medator does not also own the goods avalable n the market. The arguments of the prevous secton suggest that central rental mechansms may fal to operate well because the renter lacks any control over qualty evaluatons. Whereas ths may be allevated n the central case through adopton of a reputaton mechansm [Dellarocas, 2003, Fredman et al., 2007, Josang et al., 2007], our focus here s to examne whether central aggregaton of

7 Peer-to-Peer Tangble Goods Rental 7 reputaton nformaton can be avoded n a peer-to-peer context. Our hypothess s that peer-to-peer rental, central transfer mechansms may ncentvze o to report truthfully by offerng ntramarket recourse to renters. We thus focus on the desgn of a peer-to-peer rental, peer-to-peer transfer mechansm whch does not appeal to explct reputaton-based methods. In the proposed peer-to-peer rental, peer-to-peer transfer mechansm, ρ 0 obtans g from o, and ρ +1 obtans g from ρ. When ρ receves g, she reports ˆq n before usng g. When fnshed, she reports ˆq before transferrng g to ρ +1. Fgure 2 depcts ths sequence of events. from ρ 1 q : q n ˆq : ˆq 1 ρ receves g, reports ˆq n q : q n ˆq : ˆq n q of g degrades probablstcally q : q ˆq : ˆq n ρ fnshed usng g, reports ˆq q : q ˆq : ˆq to ρ +1 Fg. 2. Sequence of events n the peer-to-peer rental, peer-to-peer transfer mechansm from the perspectve of ρ. Each box represents the state of g at each stage, where q s true qualty, and ˆq s reported qualty. As n other mechansms, ρ pays pˆq n and receves value v q n. Two devaton penaltes penalze ρ for reportng ˆq dfferently from ρ 1 or ρ +1. Frst s the penalty n n ˆq for reducng ˆq by ˆq upon reportng ˆqn, and second s the penalty n ˆq to ρ when ρ +1 reduces ˆq by ˆq. These penaltes are strctly postve when ˆq > 0, and are zero when ˆq = 0. In addton, n n ˆq = 0 when ˆqn = 0 regardless of the value of ˆq. Also as n other mechansms, a depost dˆq n s taken from ρ for not returnng g. A reward rˆq n +1 s gven to ρ, for whch rˆq < pˆq. Note that when ˆq n = 0 or ˆq = 0, g s mmedately returned to o. In the followng, we analyze the decson faced by ρ takng as fxed the strateges of other agents; that s, we examne ρ s best response. The come to ρ s condtonally ndependent of other agents, gven ts own acton as well as those mmedately pror ( 1) and succeedng ( + 1). The reportng actons of agent 1 are drectly observed, so we can formulate ρ s decson problem n terms of a best response to ρ +1 s strategy n reportng ˆq +1 n. The mxed strategy of ρ +1 takes the form: Pr(ˆq +1 n q, ˆq ). Hereafter, we take the gven varables q ρ +1 s strategy. Gven the ρ +1 strategy Pr(ˆq n reportng ˆq s E[u ρ ˆq 1, q n, ˆq n, q, ˆq ] = v q n pˆq n and ˆq as mplct n descrbng +1 ), the expected utlty of ρ upon ˆq +1 n ˆq n n ˆq θ 1 t θ p (1) ˆqn Pr(ˆq n +1)[rˆq n +1 n ˆq ˆq ]. +1 n

8 8 James A. Hll, Mchael P. Wellman We also take as mplct the varables ˆq 1, qn, ˆq n, and q n all followng uses. Expected utlty of the renter upon reportng ncomng qualty s gven wth reference to d. The expected utlty of ρ upon reportng ˆq n s E[u ρ ˆq 1, q n, ˆq n ] = v q n pˆq n q q n n n ˆq 1 ˆqn ˆq +1 n ˆq θ t θ p δ q n q Pr(ˆq +1)[rˆq n n +1 n ˆq ˆq +1 n wth gven varables ˆq 1 and qn taken as mplct n followng uses. If reports are truthful, the expected utlty of o s E[u o q n ] = p q n q q n δ q n q (E[u o q+1 n = q E[u o q max ] = c q max θ t θ p + E[u o q n 0 = q max ]. The goal of ncentvzng ρ to report truthfully s expressed by ˆq ˆq n = ˆq = ˆq n = mn {q, ˆq n }, = mn {q n, ˆq 1}. ] r q n +1 ), Gven the exogenous parameters v, δ, θ t, and θ p, we set the mechansm parameters p, n n, n, d, and r n order to ncentvze truthful reports, the return of the good, and voluntary partcpaton. Truthful reports are strctly ncentvzed by the constrants E[u ρ E[u ρ where ˆq ˆq ˆq n = ˆq ] > E[u ρ ˆq = ˆq n ] > E[u ρ ˆq n = ˆq ] ; ˆq n = ˆq n ] ; ˆq >0 q 1 >0 q n ˆq ˆq n ],, (2) ˆq n ˆq, (3) 1 s an gong qualty report that s not truthful, and ˆq n s an ncomng qualty report that s not truthful. In the case of truthful reports, ρ s ncentvzed to return g by the constrants n rˆq > c q +1 dˆq n ; ˆq n >0 ˆq n +1 ˆq n. (4) Indvdual ratonalty constrants for ρ, agan for the case of truthful reports, are E[u ρ ˆq n = ˆq n, ˆq and ndvdual ratonalty constrants for o are = ˆq ] 0 ; q n, (5) E[u o q max ] 0 ; q max, (6) E[u o q n ] 0 ; q n. (7) The nequaltes (6) ncentvze ntal partcpaton, and (7) ncentvzes contnued partcpaton upon every subsequent rental.

9 Peer-to-Peer Tangble Goods Rental 9 Proofs of the followng propostons are avalable n the Appendx. Proposton 1 establshes that ρ s best response to a gven value for the ncomng report of ρ +1 s to match that report. In partcular, gven that the next renter reports truthfully, the current renter should report gong qualty truthfully. Proposton 1 Gven ˆq n +1, the optmal gong report of ρ s ˆq n +1 ˆq = ˆq n +1., that s, Ths result further entals that the constrants (2) on truthful gong reports are automatcally satsfed when the constrants (3), whch ncentvze truthful ncomng reports, are satsfed. Proposton 2 states that, gven that the gong report of the prevous renter s truthful, the ncomng report of the next renter s truthful, and the ncomng qualty of g s non-zero, then a specfed set of constrants on mechansm parameters s suffcent for truthful reportng of ncomng qualty. These constrants ncentvze the renter to report truthfully by ensurng that the reduced payment of a lower report s offset by a penalty for reducng reported qualty and the reducton of expected future reward. Proposton 2 Suppose ˆq 1 = ˆq 1, ˆqn all nontruthful ncomng reports 0 < ˆq n satsfy the followng constrants: n n ˆq 1 ˆqn q q n v q n δ q n q pˆq n [rˆq n = ˆqn +1 < ˆq n r mn { ˆq n q q n δ q n q Then the optmal ncomng report s truthful, ˆq n, and qn > 0, and that for, the penaltes and payments,q }] > n pˆq p ˆq n, (8) n rˆq > 0. (9) +1 = ˆq n. Proposton 3 states that renters wll report truthfully when the ncomng qualty of g s zero, regardless of the reports of the prevous and next renters. Proposton 3 Gven q n that s, ˆq n = ˆq n. = 0, the optmal ncomng report of ρ s also zero, Taken together, the three Propostons establsh that reportng truthfully s a Nash equlbrum, assumng the nequaltes of Proposton 2 are satsfed. We llustrate the calculaton of mechansm parameters for an example scenaro. Consder rentng the book Artfcal Intellgence: A Modern Approach, 3d Edton (AIMA), by Stuart Russell and Peter Norvg, for 120 days. On Amazon, the sale prces of AIMA are $117 n new/lke-new condton and $85 n good/acceptable condton. In our model, new/lke-new condton corresponds to q = 2, and good/acceptable condton corresponds to q = 1. Accordng to prces aggregated from sx textbook rental web stes, a new or lke-new condtoned AIMA costs $0.48 per day to rent. Accordng to lsted prces on a used book ste, the value of ths book dmnshes by 7% between new/lke-new/verygood and good/acceptable condtons. We assume that the consumer s value of

10 10 James A. Hll, Mchael P. Wellman usng the book s somewhat hgher than the observed prce of rental. The book s 10.4 by 8.4 by 1.9 nches n sze, and weghs 4.4 pounds, whch costs $11 to shp domestcally va U.S. Postal Servce. We further set q max = 2 to mantan a presentable number parameters. Table 1 presents the exogenous parameters of ths scenaro. c 2 c 1 v 2 v 1 δ 2 2 δ 2 1 δ 2 0 δ 1 1 δ 1 0 θ t θ p Table 1. Exogenous parameters for the AIMA rental example. We calculate mechansm parameters through lnear programmng, to maxmze partcpant expected utlty subject to mechansm and ncentve constrants. Specfcally, we ncorporate the constrants (3), (4), (5), (6), (7), and the base mechansm constrants. We present result for two objectve functons, owner expected utlty when q = q max and renter expected utlty when q n = q max, yeldng two sets of canddate mechansm parameters. The mechansm parameters presented n Table 2 satsfy the specfed constrants, assumng that the next renter reports truthfully, ˆq +1 n = ˆqn +1. In other words, we exhbt mechansm parameters under whch ratonal agents have the ncentves to partcpate, and report truthful qualtes n Nash equlbrum. Objectve p 2 p 1 r 2 r 1 d 2 d 1 n n 2 n n 1 n 2 n 1 max E[u o] max E[u ρ] Table 2. Mechansm parameters ncentvzng the truthful reportng equlbrum, return of g, and voluntary partcpaton. Next, we examne the robustness of the mechansm parameter settngs by supposng that the next renter reports ncomng qualty ˆq +1 n truthfully wth only some probablty, m. The full reportng strategy s descrbed condtonal on all combnatons of true qualty and gong ρ reports n Table 3. We calculated mechansm parameters for m {1, 0.99, 0.9, 0.8,..., 0.1, 0.01}. As m was decreased, the lnear constrants used n each optmzaton were accumulated for use n subsequent optmzatons. At each level of m, we verfed that the resultng parameters were vald for all greater values of m. Calculated values when m = 0.5 and m = 0.01 are presented n Table 4.

11 Peer-to-Peer Tangble Goods Rental 11 q ˆq ˆq n +1 Pr(ˆq n +1 q m m m (1 m) (1 m) m m (1 m) m (1 m) m m (1 m) (1 m) m, ˆq ) Table 3. Probabltes of ˆq +1 n gven q and ˆq, where m controls truthfulness. 7 Conclusons Our game-theoretc examnaton of tangble prvate goods rental suggests that ncentves for accurate qualty reportng depend on the organzaton of the market as well as key mechansm parameters. For mechansms n whch the owner of goods s also the prncpal of the market, we observed that the owner s motvated to msrepresent the qualty of the good after the renter has returned t. More constructve s our fndng that mechansms n whch the prncpal s a thrd-party to the transacton can nduce ncentve compatblty. The verson of such a mechansm n whch the good s transferred ndrectly between renters may acheve ncentve compatblty wth the mplementaton of reputaton-based mechansms, whch gve ntramarket recourse to renters. The man contrbuton of ths work s a novel mechansm n whch the prncpal s a thrd-party and goods are transferred drectly between renters. We showed that wth ths mechansm, ncentve compatblty can be acheved wth explct management of partcpant reputaton. Ths mechansm mnmzes the number of tmes the good s transferred, typcally a sgnfcant cost for onlne tangble goods rental mechansms. A drawback of the approach s that the mechansm parameters (payments and penaltes) must be talored to the envronment, whch may be nformatonally expensve due to the need to assess exogenous doman-specfc features. Future work should evaluate the senstvty of mechansm propertes to such factors, as well as the potental and mplcatons of multple equlbra.

12 12 James A. Hll, Mchael P. Wellman m Objectve p 2 p 1 r 2 r 1 d 2 d 1 n n 2 n n 1 n 2 n max E[u o] max E[u ρ] max E[u o] max E[u ρ] Table 4. Calculated mechansm parameter values optmzed for maxmum owner expected utlty when q = q max and renter expected utlty when q n = q max as m s vared. Appendx A: Proof of Proposton 1 Gven ˆq +1 n, expected utltes of ρ upon reportng ˆq are E[u ρ E[u ρ E[u ρ ˆq +1, n ˆq = ˆq +1] n = v q n pˆq n +rˆq n +1 ˆq +1, n ˆq > ˆq +1] n = v q n pˆq n +rˆq n +1 n ˆq +1, n ˆq < ˆq +1] n = v q n pˆq n +r <ˆq n +1. n n ˆq θ 1 t θ p ˆqn n n ˆq θ 1 t θ p ˆqn >ˆq +1 n ˆqn +1 n n ˆq θ 1 t θ p ˆqn ˆq > ˆq n +1 when E[u ρ ˆq +1, n ˆq > ˆq +1] n > E[u ρ ˆq +1, n ˆq = ˆq +1] n 0 > n >ˆq. +1 n ˆqn +1 n 0 by defnton, and thus ˆq ˆq +1 n. ˆq < ˆq +1 n when E[u ρ ˆq +1, n ˆq < ˆq +1] n > E[u ρ ˆq +1, n ˆq = ˆq +1] n r <ˆq n +1 > rˆq n +1. r <ˆq n +1 < rˆq n +1 by defnton, and thus ˆq = ˆq +1 n.

13 Appendx B: Proof of Proposton 2 Gven ˆq 1 = ˆq 1, ˆqn are ˆq n ˆq n and E[u ρ = ˆq n E[u ρ ˆq n when n n ˆq 1 ˆqn v q n E[u ρ +1 = ˆqn +1 ˆq n Peer-to-Peer Tangble Goods Rental 13, and qn > 0, the expected utltes of ρ gven = ˆq n ] = v q n n pˆq q q n (0, ˆq n )] = v q n p ˆq n δ q n ˆq n q q n pˆq n q q n = 0] = θ t θ p E[u ρ δ q n q E[u ρ q q n ˆq n [rˆq n +1 ˆq n δ q n q n n θ ˆq t θ p 1 ˆqn δ q n q rˆq n +1 n n θ ˆq t θ p 1 ˆqn q r mn { ˆq n,q } = ˆq n ] > E[u ρ ˆq n (0, ˆq n )] r mn { ˆq n,q }] > n pˆq p ˆq n = ˆq n ] > E[u ρ ˆq n = 0] n rˆq > Appendx C: Proof of Proposton 3 Gven q n ˆq n E[u ρ E[u ρ = ˆq n E[u ρ = 0, the expected utltes of ρ gven ˆq n q n q n when q n = 0, ˆq n = 0, ˆq n = 0, ˆq n. Thus, the rght-hand sde of In- By defnton, rˆq n +1 < pˆq n equalty 10 s negatve, and ˆq n = ˆq n ] = θ t θ p > ˆq n ] = p >ˆq n ˆq +1 n ˆq are n n θ ˆq 1 t θ p >ˆqn P r(ˆq +1)[rˆq n n +1 n = ˆq n ] > E[u ρ q n = 0, ˆq n > ˆq n 0 > p >ˆq n for all ˆq n ˆq +1 n ˆq +1 ˆqn = ˆq n n n ˆq 1 >ˆqn P r(ˆq +1)[rˆq n n +1 n ˆq ˆq +1 n ]. ] (10) ˆq ˆq +1 n gven q n = 0. ].

14 Bblography George A. Akerlof. The market for lemons : Qualty uncertanty and the market mechansm. Quarterly Journal of Economcs, 84: , Russell Belk. Sharng. Journal of Consumer Research, 36: , Yocha Benkler. Sharng ncely: On shareable goods and the emergence of sharng as a modalty of economc producton. Yale Law Journal, 114: , Rachel Botsman and Roo Rogers. What s Mne Is Yours: The Rse of Collaboratve Consumpton. Harper Busness, Chrysanthos Dellarocas. The dgtzaton of word-of-mh: Promse and challenges of onlne reputaton mechansms. Management Scence, 49: , Jeffrey F. Durgee and Gna Colarell O Connor. An exploraton nto rentng as consumpton behavor. Psychology and Marketng, 12:89 104, Mchal Feldman, Chrstos Papadmtrou, John Chuang, and Ion Stoca. Freerdng and whte-washng n peer-to-peer systems. IEEE Journal on Selected Areas n Communcatons, 24: , Erc Fredman, Paul Resnck, and Rahul Sam. Manpulaton-resstant reputaton systems. In Noam Nsan, Tm Roughgarden, Éva Tardos, and Vjay V. Vazran, edtors, Algorthmc Game Theory, pages Cambrdge Unversty Press, Garrett Hardn. Tragedy of the commons. Scence, 162: , Audun Josang, Roslan Ismal, and Coln A. Boyd. A survey of trust and reputaton systems for onlne servce provson. Decson Support Systems, 43: , Cat Poynor Lamberton and Randall L. Rose. When s ours better than mne? a framework for understandng and alterng partcpaton n commercal sharng systems. Journal of Marketng, Stephane J. Lawson. Forsakng Ownershp: Three Essays on Non-Ownershp Consumpton and Alternatve Forms of Exchange. PhD thess, Florda State Unversty, 2011.