IMPLEMENTATION IN PUBLIC ADMINISTRATION OF MEXICO GOVERNMENT USING GAMES THEORY AND SOLVING WITH LINEAR PROGRAMMING

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1 Itertol Jourl of Advces Egeerg & Techolog, J., 05. IJAET ISSN: 96 IMPLEMENTATION IN PUBLIC ADMINISTRATION OF MEICO GOVERNMENT USING GAMES THEORY AND SOLVING WITH LINEAR PROGRAMMING Frcsco Zrgoz Huert. Idustrl Egeerg Deprtmet. ITESM Cmpus Irputo. Méxco. ABSTRACT Ths pper shows how to mplemet s egottg wth trde uos clled STASPE (workers emploed b the executve brch) Mexco Govermet wth the publc dmstrto c be performed usg methodolog clled gme theor d beg solved wth ler progrmmg through the mplemetto wth structured lgorthms lke Gms, (Geerl Algebrc Modellg Sstem) softwre. A cretve, geous d prctcl w d modelg tool s cheved wth poloml tme respose lvsh. Ths mplemetto c be used b govermets, eterprses busesses s well s prtershps to stregthe ther strtegc decsos. The use of scece s w to solve coflcts should be pth to the professolzto d compettveess sde publc sttutos Mexco d other coutres. KEY WORDS: Optmzto, Gmes Theor, Uo, Strteges, Mtrx, Vlues, STASPE I. INTRODUCTION Gme Theor ws creted b Vo Neum d Morgester 9 hd tcpted some des. Ecoomsts such s Courot d Edgeworth were prtculrl ovtve the eteeth cetur. Other scholrs d scholrs lso mde mportt cotrbutos mog whch we meto the Zermelo Borel d mthemtcs. I the erl fftes, umber of ver fmous mthemtcs Joh Nsh tems broke two brrers tht Vo Neum d Morgester were self-mposed. Gme Theor curretl hs m pplctos, mog dscples re: Pscholog focused o geder, Ecoomcs, Poltcl Scece, Bolog d Phlosoph d s ver fertle feld of publc dmstrto where the use of ths methodolog llows for extremel compettve dvtges optmzg resources d brod vso to cheve complce gols d obectves. Ech er publc sttutos must revew slr creses s well s the beefts to be grted to emploees, hve bee perodcll coducted through greemets betwee leders wthout cosderg scece s w of fdg the best soluto for both sdes, s here where rses the teto to use uusul methodolog s w of soluto to lbor dsputes betwee publc sttutos d publc servce workers. Rememberg, how Gme theor s pproch to uderstdg hum behvor tht coceves of decso-mkers s plers gmes. Most stutos we fce do't come wth book of rules lke the oes for prlor gmes or sportg evets. But gme theorst tres to desg rules tht cpture the costrts fced b decso-mkers d sks "Wht ctos would be chose b plers fcg these rules?" If the predcted ctos re smlr to the behvor of rel-lfe decso-mkers, the the model helps us "uderstd" tht behvor. B other hd t s mportt to strt the use of scetfc tools lke gme theor represeted cross the ler model tht llows the serch for compettveess publc sttutos Mexco. Trdtoll 6 Vol. 7, Issue 6, pp. 6-68

2 Itertol Jourl of Advces Egeerg & Techolog, J., 05. IJAET ISSN: 96 the publc sttutos hve ot bee gol. Addtoll the serch for clrt egottos wll gve trsprec d m coflcts whch geerll results the strke of emploees the publc sector. Orgl d uusul de s show the form of qult mgemet d lookg for soluto wth the frmework of optmzto re. The orglt could be poeer kd of mplemetto tools ot ol Mexco d Lt Amerc too. II. OBJECTIVE The m purpose of mke mplemetto gme theor sde publc Isttutos s to estblsh gudele to professolzto d trsprec sde rtol processes strtegc stutos whch re smulted relt gmes evets clled processes, whch volve rtol people lookg for mprovemet lbor rghts geertg competto beod the ow commo sese. The Strteges; A smulto publc sttutos through gme theor whch uses strteges c be defed s specfc set of rules tht s wht plers c do ll possble crcumstces. The gme s pled deomted shres tht re subect to rules to cheve the gol, prtculr solve coflcts betwee workers d Drectors d Mgemets. I our problem the m ssumpto s tht ll the plers (Emploers d Publc Isttutos Drectors) who prtcpte tr to use rtol tttude d lws followg the coservtsm crtero to mxmze profts or mmze losses. The poff mtrx represets the mouts tht pler c w or lose bsed o ther opo, represeted qutttve mer tht wll mesure performce. Gme theor s lked to the ler progrmmg d the cse of two Perso zero-sum c be rsed s ler progrmmg problem. I these gmes pler ttempts to mxmze pmet whle trg to mmze s pg hs oppoet, the zero-sum gme two pler J s the row pler d J s the colum pler. The complete soluto of set of strteges cludes: ) The vlue of pl b) The optml strteges for ech pler III. LITERATURE REVIEW Gme Theor Evolutor Revsg the stte of rt we foud the theor of evolutor gmes cotues to grow. M pure gme theorsts beleve tht ths s ot true theor of gmes, sce the ctors re ctull preprogrmmed mechsms. However, sese, these mechsms c be cosdered resoble models wth lmted rtolt gets. Also there re good possbltes to exme the expermetl evdece for the predctos of evolutor gme theor: bsc bolog d the stud of ml behvor offer cosderble groud for lrge-scle smultos where the msses of gets re stll reltvel smple behvorl rules to vod coflcts. The m s to uderstd the problems sted of worrg bout the sttus of methodologcl procedure. The gme theor evolutor could be complemetr prt process of rtol strtegc lss betwee hums tht seek to solve problems of thousds of people, lss of the w he s thkg d ctg c be trsformed to processes tht provde qutttve vlues to fll the mtrx egottos Cber Theoretcl work of Rubste (986, Nem d Okd (00) re mportt. You eed to keep expermetg wth rtfcl plers zero sum gmes (but lso those wth o-zero sum), sce ths work shows us mportt sghts d comprsos betwee hums d mches. The work of Arthur AA.VV. (997) whch smultes dvduls choosg mog collecto of heurstc rules to the extet the re lerg mrket, offers pproch to the problem of how bod lers to choose expecttos d prces the stock mrket. Ths s dctve of ew drectos tht the pursts would ot cosder gme theor, but potg to the hert of the problem: competto d cooperto, ol from dfferet perspectve. The stud of gme theor hs gve us powerful lguge tht hs helped us to exme some of the problems fced b coscous optmzg gets compettve stutos how s to vod workers o strke. The success of these pplctos hs show ts lmts. Altcl d computtol 6 Vol. 7, Issue 6, pp. 6-68

3 Itertol Jourl of Advces Egeerg & Techolog, J., 05. IJAET ISSN: 96 requremets, we wll show the w to solve these problems. The prdoxes tht pper betwee dvdul rtolt d socl rtolt d dcte the dffcult of potg the rght soluto for set of people. The growg evdece of how dvduls behve expermetl gmes d terest to uderstd the competto d cooperto betwee cells, sects, plts d other lvg orgsms dctes the drecto of future developmet of gme theor. It s ver mportt to meto tht we dd ot fd evdece the lterture of Lt Amerc bout mplemetto usg gme theor sde publc sttuto s w to tke decsos wth trsprec to professolzto, where t hs used how scetfc tool or ltertve to solve lbor problem, where both prtes come to the soluto of coflcts wth rtol strteges mplemeted to the mthemtcl progrmmg s w of modelg d soluto poloml tme. Ths s oe of the resos wh t s showg s useful d prctcl w mkg tellget decsos publc dmstrto d we c thk tht t could be ppled to prvte sttutos. IV. METHODOLOGY Ler progrmmg s mportt feld of optmzto for severl resos; m prctcl problems opertos reserch c be stted s ler progrmmg problems. Some specl cses of ler models, such s gmes theor were cosdered the developmet of mthemtcs mportt eough b themselves to geerte much reserch o speclzed lgorthms for ther soluto. A seres of lgorthms desged to solve other optmzto problems re specl cses of the broder techque of ler progrmmg. Hstorcll, des from ler progrmmg hve spred m of the cetrl cocepts of optmzto theor, lke gmes theor mplemetto d of course dult, decomposto, d the mportce of covext d ts geerlztos. I our reserch pper we hve formulted the hpothess tht scetfc tool s t s gme theor ler progrmmg c help resolve dsputes regrdg to professolzto usg cotedg opos d trsltg them to percetges possblt to use prtculr strteg, provdg dfferet optos to get the best results ccordg to ther terests. I order to show solutos usg scetfc tools lke gme theor whch coves the results of the egottos? I our reserch pper we hd to detf ltertves to estblsh the mtrx of egotto, four levels d chose oe tht would represet the logcl pot, the legl, the optmstc pot d the techcl pot s set of strtegc perceptos. The vlues wth the mtrx of egotto were obted through vergg the weghts of opo of the prtcpts o both sdes s fucto of ther kowledge, experece d terests. The tool show s tmeless becuse t wll be possble to use t ech ul perod uthort d workers gther to updte slres d beefts for emploees of the publc sttuto. Mx, z v Subect, to... v v v 0,,,, v, urestrcted Tble I: The gme model usg ler progrmmg for the pler J s 6 Vol. 7, Issue 6, pp. 6-68

4 Itertol Jourl of Advces Egeerg & Techolog, J., 05. IJAET ISSN: 96 Mx, z w Subect, to... w w w 0,,,, w, urestrcted Tble II. The gme model usg Ler Progrmmg for the pler J s: The formto mtrx hs cresed the level expected for ech of the vews betwee the Uo (d the pprovl bod STASPE Uo Stte through the Mstr of Admstrto) performce. Ths s mplemeted the progrm merts. The crese performce ssessmet percetges expected bck to trg receved b publc Servts d publc servers o the premses of the Executve Servce show the followg tble: Tble III. STASPE uo opo / Govermet Opo Logcl (b) Legl (b) Optmstc (b) Techcl (b) Logcl () Legl () Optmstc () Techcl () It geertes the followg Questo: Whch ltertve should the Uo cosder? Ad whch ltertve should the govermet cosder? Usg the methodolog of gme theor. The Optml Expected Performce Servce persoel executve. Tht ou c see how s ot possble Rechg Brekeve. v.5 v v So ou eed to mplemet rdomzed strteges Now we pose the ler progrmmg problem ssocted to the gme Cosder : x probblt, choo s g, probblt, choo s g, b Tble IV. 65 Vol. 7, Issue 6, pp. 6-68

5 Itertol Jourl of Advces Egeerg & Techolog, J., 05. IJAET ISSN: 96 ForUo, STASPE Mmze, w subec, to ,,,... w, urestrcted subect, to 0.0x 0.0x 0.50x 0.5x x x x x v, urestrcted Mxmze, v 0.0x 0.0x 0.5x 0.0x for, Govermet : x ,,,... m 0.5x 0.55x 0.0x x x 0.x 0.8x w w 0.5x w w v v v v Tble V. Code for the ler Progrmmg Model usg softwre GAMS *Implemetto of gmes theor usg ler progrmmg Publc Admstrto Mexc Govermet * Performce Dr. Frcsco Zrgoz Huert *October 0 / */ / *5/ ; Prmeters b() / /; Prmeters c() / /; free vrbles z, w postve vrbles () tble A(, ) Vol. 7, Issue 6, pp. 6-68

6 Itertol Jourl of Advces Egeerg & Techolog, J., 05. IJAET ISSN: Equtos fo Obectve Fucto Rest() costrt oe Rest costrt two; fo.. z =e= w; Rest().. sum (, A(, )*())-w=l= b(); Rest.. sum(,())=e=; OPTION OPTCR=0.0000; Model eerc /ll/; Solve eerc usg LP mmzg z; GENERATION TIME = 0.00 SECONDS S O L V E S U M M A R Y Tble VI. Expermetl Results usg Gms Softwre TYPE LP DIRECTION MINIMIZE SOLVER CPLE FROM LINE 5 MODEL eerc OBJECTIVE z **** SOLVER STATUS NORMAL COMPLETION **** MODEL STATUS OPTIMAL **** OBJECTIVE VALUE Optml soluto foud. Obectve: LOWER LEVEL UPPER MARGINAL INF... +INF INF INF. V. CONCLUSIONS The expected crese the performce evluto of publc servts d publc For the stte pprovl bod optos re: (0.75, 0, 0, 0.5) Therefore we c coclude tht both the Uo d the Stte should choose the ltertve. (Opo Logcl, Opo Logcl) To cheve optml ehcemet of 8.75% o the expected work performce Publc Servce Emploers hve 8.75% For the STASPE Uo the optos re: (0.75, 0, 0.5, 0) We c see how ws possble to fd soluto to both prtcpts usg scetfc tool clled gmes theor s ltertve to promote professolzto d trsprec mgemet decsos. Lmtg the use of the tool wll be trsprec d the tttudes of prtcpts hve s w to brg clrt d trsprec to the dmstrtve process of settg ul work beefts. The hpothess metoed the methodolog could be ccepted becuse the results get obted for ech strteg of prtcpts to be stsfed llowed terms of ther chces d wre tht the best opto s free of corrupto d get obted from cler d trspret 67 Vol. 7, Issue 6, pp. 6-68

7 Itertol Jourl of Advces Egeerg & Techolog, J., 05. IJAET ISSN: 96 w d the process wll be fr d equtble tht could be updted ech perod usg scetfc tool lked to ler progrmmg usg theor of gmes. The pper presets orgl progrmmg code to fd the vlue of the gme d the chces for ech prter strteg of cotestts, the code t s effcet d prctcl d could be workg o lrge scle model. I. Suggestos d Recommedtos.. The use of gme theor usg ler progrmmg s smple d prctcl tool for mplemetto s well s ecoomcl publc dmstrto.. The use of scece orgztos reduces ucertt strtegc decso mkg. The exteded model llows lrge-scle optmzto rel-tme solutos.. Scece s w to professolze sttutos 5. The mzg speed gms softwre d rutmes re mzg ust 0.00 secods REFERENCES []. Ahu R.K.,T.L.,Mgt, d J.B.Orl, Networks Flows: Theor, Algorthms,d Applctos;Pretce Hll,Eglewood Clffs, NJ,00. []. Hgle,J..L. d S.W.Wllce, Sestvt Alss d Ucertt Ler Progrmmg, Iterfces,(),pp.5-66,00. []. Akgul,M., A ote o Shdow Prces ler Progrmmg Jourl of the Opertos Reserch Socet,5(5),pp,5-,98 []. Al A,R,Helgso,J,Kegto,dH,Lll, Prml Smplex Network Codes:stte-of-thertImplemetto Techolog, Networks,8,pp,5-9,978 [5]. Asher,D,T, A Ler Progrmmg Model for the lloctoof R d D efforts, IEEE Trsctos o Egeerg Mgemet,EM-9(),PP.5-57,December 99. [6]. Bllsk,M.L. A Compettve (Dul) Smplex Method for Assgmet Problem Mthemetcl Progrmmg,(),pp.5-,986). [7]. Bres,J,W,d R.M.Crsp, Ler Progrmmg: A Surve of Geerl Purpose Algorthms, AIIE Trsctos,7(),pp.-,September 975. [8]. Brr,R,S,F,Glover, d D.Klgm, The Altertve Bss Algorthm for Assgmet Problems, Mthemtcl Progrmmg,(),pp.-, Vol. 7, Issue 6, pp. 6-68