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Topic: Is Collusion Possible?

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S ude : Ma yukhi A o , 2 group. eacher: Alla Friedma . Международный Институт Экономики и Финансов, 3 курс. Высшая Школа ЭкономикиEssay i Microeco omics. opic: Is Collusio Possible?18.12.2000Co e s: I roduc io . wo ypes of behaviour (Collusive a d o -collusive). Game heory. Co cep . he problem of collusio . Preda ory prici g. Repea ed games approach. Co cep . Fi i e game case. I fi i e game case. “ rigger” s ra egy i -for- a . d.) Fi i e game case, Kreps approach. he mo ives for re alia io . Co clusio . Bibliography. I roduc io . I his essay I would discuss he price a d ou pu de ermi a io u der he o e esse ial ype of imperfec compe i io marke s- oligopoly. I er-firm i erac io s i imperfec marke s ake ma y forms. Oligopoly heory, hose ame refers o “compe i io amo g he few”, lack u ambiguous resul s of hese i erac io s u like mo opoly a d perfec compe i io . here is a varie y of resul s derived from ma y differe behavioural assump io s, wi h each specific model po e ially releva o cer ai real-world si ua io s, bu o o o hers. Here we are i eres ed i he s ra egic a ure of compe i io be wee firms. “S ra egic” mea s he depe de ce of each perso ’s proper choice of ac io o wha he expec s he o her o do. A s ra egic move of a perso i flue ces he o her perso ’s choice, he o her perso ’s expec a io of how would his par icular perso behave, i order o produce he favourable ou come for him. wo ypes of behaviour (Collusive a d o -collusive). Models of e erprise decisio maki g i oligopoly derive heir special fea ures from he fac ha firms i a oligopolis ic i dus ry are i erdepe de a d his is realised by hese firms. Whe here are o ly a few producers, he reac io of rivals should be ake i o accou . here are wo broad approaches o his problem. Firs , oligopolis s may be hough of as agreei g o co-opera e i se i g price a d qua i y. his would be he Collusive model. Accordi g o his model, firms agree o ac oge her i heir price a d qua i y decisio s a d his would o exac ly he same ou come as would have bee u der mo opoly. hus he explici or co-opera ive collusio or Car el would ake place. Seco d approach of he oligopoly a alysis is based o he assump io ha firms do o co-opera e, bu make heir decisio s o he basis of guesses, expec a io s, abou he variables o which heir compe i ors are reachi g a d abou he form a d he a ure of he reac io s i ques io . he o -collusive behaviour deals wi h his model. Here, hough i equilibrium he expec a io s of each firm abou he reac io s of rivals are realised, he par ies ever ac ually commu ica e direc ly wi h each o her abou heir likely reac io s. he ex reme case of his ca eve imply compe i ive behaviour. Such a si ua io is much less profi able for firms ha he o e i which hey share he mo opolis ic profi . he purpose of his paper is o a alyse he case of he possibili y of collusio be wee firms i order o reach he mo opolis ic profi s for he i dus ry, assumi g ha hey do o co-opera e wi h each o her. his would be he mos i eres i g a d ambiguous case o look a . Game heory.

a.) Co cep . he o io of game heory would a good s ar i g poi i he s udy of s ra egic compe i io a d would be very helpful i realisi g he model a d he problems faci g oligopolis ic firms associa ed wi h i . Game heory provides a framework for a alysi g si ua io s o which here is i erdepe de ce be wee age s i he se se ha he decisio s of o e age affec he o her age s. his heory was developed by vo euma a d Morge s er a d describes he si ua io , which is ra her like ha fou d i he childre ’s game “Scissors&S o es”. Each firm is ryi g o seco d-guess he o hers, i.e. he behaviour of o e firm depe ds o wha i expec s he o hers o do, a d he i ur are maki g heir decisio s based upo heir expec a io s of wha he rivals (i cludi g he firs firm) will do. I our case, he players of he game are he firms i he i dus ry a d each of hem wa s o maximise i s pay-off. he pay-off ha a player receives measures how well he achieves his objec ive. Le ’s assume i our model he pay-off o be a profi . heir profi s depe d upo he decisio s hey make ( he s ra egies chose by he various players i cludi g hemselves). A s ra egy i his model is a pla of ac io , or a comple e co i ge cy pla , which specifies wha he player will do i a y of he circums a ces i which he migh fi d himself. he game also depe ds o he move order a d he i forma io co di io s. Games ca be ca egorised accordi g o he degree of harmo y or disharmo y be wee he players’ i eres s. he pure coordi a io game is he o e ex reme, i which players have he same objec ives. he o her ex reme is he pure co flic of he opposi e i eres s of players. A d usually here is a mix ure of coordi a io a d co flic of i eres s- mixed mo ive games. Al hough he impor a ce of he o her players’ choices akes place, some imes a player has a s ra egy ha is he bes irrespec ive of wha o hers do. his s ra egy is called domi a , a d he o her i ferior o es are called domi a ed. A si ua io i which each player is choosi g he bes s ra egy available o him, give he s ra egies chose by o hers, is called a ash equilibrium. his equilibrium correspo ds o he idea of self-fulfilled expec a io s, aci , self-suppor i g agreeme . If he players have somehow reached ash equilibrium, he o e would have a i ce ive o depar from his agreeme . A y agreeme ha is o a ash equilibrium would require some e forceme . b.) he problem of collusio . ow I would like o use a example of a game i which he Cour o ou pu decidi g duopoly is i volved. his game is illus ra ed by he able below: Firm B’s ou pu level HIGH LOW Firm A’s ou pu level HIGH (1;1) (3;0) LOW (0;3) (2;2) Here a firm chooses be wee wo al er a ives: high a d low ou pu s ra egies. he correspo di g pay-offs (profi s) are give i he boxes. I his game, he bes hi g ha ca happe for a firm is o produce a high level of ou pu while i s rival produces low. Low ou pu of he rival provides ha price is o drive dow oo much, hus a firm could ear a good profi margi . he wors hi g for a firm is o cha ge places wi h i s rival assumi g he same si ua io akes place. If bo h firms produce high levels of ou pu , he he price would be low, allowi g each of hem o ear s ill posi ive bu very small profi s.

ever heless, (HIGH;HIGH) would be he domi a s ra egy of his game (we would observe a ash equilibrium i s ric ly domi a s ra egies here). I is he bes respo se of firm A whe ever B produces a high or low ou pu a d his is also rue for firm B. he o -co-opera ive ou come for each firm would be o ge he pay-off of 1. Bu as we ca see, i would be be er for bo h o lower heir ou pu a d hereby o raise price, as heir profi s would i crease o 2 for each firm i s ead of 1 i E. S ra egy (LOW;LOW) would be he collusive ou come. he problem of collusio is for he firms o achieve his superior ou come o wi hs a di g he seemi gly compelli g argume ha high ou pu levels will be chose . his was a example of a “o e-sho ” game a d we saw ha he collusive ou come was o available for ha case. Bu i reali y hese games are bei g played over a d over (o a lo g- erm basis) a d we will see la er i his essay how he collusio ca be sus ai ed by hrea s of re alia io agai s o -co-opera ive behaviour. c.) Preda ory prici g. Here we eed o i roduce he explici order of moves i he model. here are agai wo players-firms o he marke - a i cumbe firm a d a po e ial e ra i he marke . he game is illus ra ed below: he po e ial e ra chooses be wee e eri g a d s ayi g ou of he i dus ry. I he case of his e eri g, he i cumbe firm ca ei her figh his e ry (which as we see would be cos ly o bo h), or acquiesce a d arrive a some peaceful co-exis e ce (which is obviously more profi able). he bes hi g for i cumbe is for e ry o o ake place a all. here are i fac wo ash equilibria: (I ;ACQUIESCE) a d (OU ;FIGH ). Bu he las me io ed (OU ;FIGH ) is implausible, as if he i cumbe were faced wi h he fac of e ry, i would more profi able for him o acquiesce ra her ha o figh he e ry. Due o his fac he po e ial e ra would choose o e er he i dus ry a d he o ly equilibrium would be (I ;ACQUIESCE). hus we ca co clude, ha i his case he i cumbe ’s hrea o figh was emp y hrea ha would ’ be believed, i.e. ha hrea was o a credible o e. he co cep of perfec equilibrium, developed by Sel e (1965;1975), requires ha he “s ra egies chose by he players be a ash equilibrium, o o ly i he game as a whole, bu also i every subgame of he game”. (I our model o he pic ure, he subgame s ar s wi h he word “i cumbe ”). We have go he perfec equilibrium o rule ou he u desirable o e. Repea ed games approach. Co cep . As I have already me io ed, i prac ice firms are likely o i erac repea edly. Such fac ors as ech ological k ow-how, durable i ves me s a d e ry barriers promo e lo g-ru i erac io s amo g a rela ively s able se of firms, a d his is especially rue for he i dus ries wi h o ly a few firms. Wi h repea ed i erac io every firm mus ake i o accou o o ly he possible i crease i curre profi s, bu also he possibili y of a price war a d lo g-ru losses whe decidi g whe her o u dercu a give price direc ly or by i creasi g i s ou pu level. O ce he i s abili y of collusio has bee formula ed i he “o e-sho ” priso ers dilemma game, i raises he ques io of whe her here is a y way o play he game i order o e sure a differe , a d perhaps more realis ic, ou come.

After sketching out a possible design with the cards, the designers moved to the workstations and wrote program matching the design, delivering a small bit of system function. The design was never written down. It lived in the cards, in memories of the conversations surrounding the cards, in the unit tests written to capture the detailed requirements, in the code, and in the shared memories of the people who had worked together on a rotating basis during the design's development. This was a group highly attuned to the cooperative game principle. Their intermediate work products, while radically minimalist, were quite evidently sufficient to the task of developing the software. The team delivered new function every three weeks over a three-year period. Sufficiency in the Residue Thus far, the topic of discussion has been the primary goal of the game: delivering working software. However, the entire project is just one move within a larger game. The project has two goals: to deliver the software and to create an advantageous position for the next game, which is either altering or replacing the system or creating a neighboring system

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