Game theory in Oligopoly

Transcription

1 Game theory n Olgopoly Prof. Marx Boopath, Nkolaj Sujen. Abstract The game theory technques are used to fnd the equlbrum of a market. Game theory refers to the ways n whch strategc nteractons among economc agents produce outcomes wth respect to the preferences (or utltes) of those agents, where the outcomes n queston mght have been ntended by none of the agents. The olgopolstc market structures are taken and how game theory apples to them s explaned. Keywords: game theory, olgopoly, market structure 1. Introducton The market structure dentfes how a market works n terms of the number of the frms engaged n, the nature of the produced product, effcency of frm etc. There are many forms of market structure and the most revealed s Olgopoly. In olgopolstc markets, there always reman a struggle between self nterest and cooperaton. If the output s lmted by all the frms, the prce becomes hgh, but t mples that then output wll be expanded because of frm s ncentve to do that. The analyss through Game theory s drectly relevant to the behavour of busnesses n olgopolstc markets. The decsons taken usng the theory about the self nterest and cooperaton decde the nvestment and spendng of the frms. Conventonal economcs descrbes the operaton of mature & establshed markets, but t throws no lght on people s creatvty n fndng new ways of nteractng wth one another. The economcs of markets s dynamc and evolvng. The nnovaton contnues and nothng s taken gven. In the rapdly and free-form transformng marketplace, game theory s the kernel of a new economcs. 2. The Olgopoly The man characterstcs of an olgopoly market are: o There are few frms to compete n. It may happen that a large number of frms are there but two very bg manufacturers domnate the ndustry. o The Concentraton Rato of the market sales s n the hand of those two producers. If they account for 90% rato of share of market sales n the ndustry t s called a 2 frm concentraton rato of 90%. The arlnes ndustry s a good example of t. o The larger of the two frms has Prce leadershp that s followed by smaller frm o Colluson Potental o Interdependence between frms Behavour s affected by actons of rvals o Goods manufactured may be ether hghly dfferentated or homogeneous o loyalty aganst brand & brandng may cause a potental source of advantage o Cournot Model suggest equlbrum n long run cause normal profts and equal market share o Use of game theory to explan behavour of the frms to a extent 1 P a g e

2 o AC curve s saucer shaped mnmum effcency may be needed to cover large range of output o Entry restrcted due to hgh barrers o Examples nclude Moody s & 3. Game theory S&P n the ratngs market, Coca cola and Peps, Vsa and Master card etc. It s a unversal language for the unfcaton of the behavoural scences. Gnts (2000, 2009). In smple words ths theory studes peoples behavour n strategc stuatons. It s the formal study of cooperaton and conflct and can be appled where the actons of several frms are nterdependent. The game theory concepts provde a language to structure, formulate, analyze and understand strategc scenaros. Edward C Rosenthal, (2011, p.18) states that Game Theory s the study of the ways n whch strategc nteractons among ratonal players produce outcomes wth respect to the preferences of those players, none of whch mght have been ntended by any of them. In a duopoly or the olgopolstc market, each frms profts depend on other frms actons resultng n the "prsoners dlemma". The prsoners' dlemma s a partcular game, whch llustrates the dffculty of cooperaton, even when t s n the best nterests to market players. The self owned domnant strateges are selected by the both market players for ther short-sghted personal profts. Eventually, equlbrum s reached where both may worse off than they would have been, f an alternatve (non-domnant) strategy could have been agreed upon between them. The fundamental assumpton of the game theory s that all players are ntellgent and ratonal and each player uses those strateges whch result n the long run equlbrum. At ths pont not anyone wants to wthdraw from ts strategc deology. In the grocery market s duopolstc competton, lke n the Australan case, the game theory s partcularly mportant as t offers Low barrers to entry wthout any lcense, any upfront cost or any nfrastructure. Because of the already present two bg bulls, most retalers avod enterng nto market because they can not afford. 3.1 Nash Equlbrum In the supermarkets duopolstc competton, lke n the Australan case, the strateges adopted are related to EDLP (everyday low prcng) and HLP (hgh low prcng) that change from week to week. Both strateges are domnant for maxmsng sales and profts wth focus on week to week sales. The strategy related to HLP s more transparent and explct, whch conssts of n store advertsng, meda advertsng, merchandsng and prce reductons. Ths strategy n game theory s shown n the followng table. As per the game theory t s a normal game between the two players. Source: An applcaton of Game theory The parameters n above table can take any values but the constrant s that each player has played the game several tmes and knows other players components of strategy whch may be dfferent. That means each player has n all nne strateges and each play requres three strateges at one tme. Thus n all there are twenty seven pay offs for ths 2 P a g e

3 there and the quantty would also be socally effcent. game. Ths mples that t would not be easy to acheve Nash equlbrum but not mpossble. The sales beng observed on weekly bass, f these are n lne wth expectatons and long run objectves of player one and f rvals are followng passve strateges then the probablty that player two too wll contnue the passve strategy s qute hgh and vce versa. The same strategy s appled for aggressve strateges also. However, wthn ths game the costs are lkely to reman low and profts may soar. In practce, however t does not happen and rvals may adopt an alternate strategy to be better off. The followng table shows the pay off matrx for nne of twenty seven strateges that are mplct n the above table. Source: An applcaton of Game theory The each cell n the above table s showng the pay off for each player for all the three dfferent strateges. The Nash equlbrum s also shown but ths level also can t be consdered as a stable equlbrum because t s attrbuted to hgher nventory and promotonal costs. If nstead of two, there are more frms n the market, the prce effect wll be smaller resultng n the lower Nash equlbrum prce. If the number of frms reaches nfnty, the prce effect wll also approach zero. So, output wll be ncreased by each seller whenever the prce moves above MC. In the end, the perfectly compettve prce wll be M. Shubk, (1968,p.) clams that The Nash equlbrum n the general game does not yeld a hgher payoff, gven the other players chosen strateges. It s a noton of jont ratonalty as each player best responds to the other players. 3.2 Bertrand Equlbrum For dfferentated products, two dentcal frms choose prces smultaneously and end up wth the stuaton lkely to perfect competton. The only pure-strategy Nash equlbrum s p 1 * = p 2 * = c because the best response s played by both frms to each other Nether frm has an ncentve to devate to some other strategy. If p 1 and p 2 > c, a frm could gan by undercuttng the prce of the other and capturng all the market. If p 1 and p 2 < c, proft would be negatve To hack wth quantty and profts, f both frms compete vcously on prce then equlbrum wll occur only where prce equals the margnal cost. Ths s because both frms are producng dentcal products and f one reduces ts prce the other wll not be left behnd and try to cut ts prce stll lower. However ths equlbrum s socally effcent as consumers wll be beneftted most. 3.3 Cournot Equlbrum If both frms become prce takers and put the prce as secondary opton and consder quantty produced they can acheve Cournot equlbrum by applyng game theory. As the product s dentcal proft maxmsaton usng quantty for one frm depends on the quantty produced by the other one. In ths model 3 P a g e

4 frms set quanttes rather than prces and each frm s own decsons are recognsed about q affect prce P/ q 0 However, each frm thnks that any other frm s not affected by ts decsons q j / q = 0 for all j For proft maxmzaton, the FOC are P Q P' Q q C' ( q ) 0 q The frm maxmzes proft where MR = MC Prce exceeds margnal cost by P' If q1 s the qty produced by one frm and q2 s the qty produced by other frm, then the total qty produced wll be q=q1+q2. Usng game theory, the soluton wll be q1=q2= (a-cb)/3, where c s the MC of the frm It can be noted that ths equlbrum s n between monopoly and olgopoly producton levels and the proft margns earned by the two frms are less than half of those as earned by the monopolst. 4. An example For example, a few, large frms domnate many Australan markets. A duopoly exsts n the grocery market of Australa, where t s domnated by Coles and Woolworths, natonally. Both of these have extensve and wde dstrbuton systems, wth many stores n almost all n regonal and urban areas across Australa. Other frms, f they wsh to enter need a large nvestment to compete wth these. In the grocery market of Australa, the seller concentraton rato s approx 80%; the two largest frms Coles and Woolworths account for 80% of total sales of groceres n Q q Australa. In a study of retal marketng Bovl (2008) stated that When you have that much (market share) you create market dstorton - a suppler who has to deal wth someone wth that much power works from a weak poston. Two retalers domnatng sales dd not qualfy as a "market" under economc defntons. In an olgopolstc market competton s ntense. Both non-prce and prce technques are used to compete. The warrantes and trcky advertsements are common aspect. As per an artcle n weekly tmes, marketng manager, Woolworths (2001), We wll not be beaten on prce. If our compettor s sellng tem X for less, we wll match ther prces, whether the tem's prce has been reduced for a specal sale or not. We wll replace the tem wthout cost f t s found to be defectve n any way. In partcular, Woolworth's has succeeded wth ts ''We're the fresh food people'' advertsng campagn. In olgopoly mutually nterdependence s a must. If polcy of prce change s adopted by one, then ths wll affect the sales of other frm n the market. Ths can be understood as follows. Suppose Coles and Woolworths ntally sell $6 per KG. Woolworths lowers ts 2prce by $1 per KG so that ts sales rse from 10,000 KG per week to 20,000 KG per week. Ths mples that at ths stage demand curve s elastc for tomatoes; the 17% decrease n prce has resulted n 50% ncrease n volume of sales. So, as Coles begns to lose ts sales to Woolworth's, to match Woolworths prce, t also reduces prce by $1 per KG. Coles does not stop here and decdes to go further by reducng ts prces to $3 per KG. The reason provded that when Woolworths decreased ts prce, t made less proft per klogram, but as many more klograms of tomatoes were sold, overall t made greater profts. If Coles do the same, t wll end up makng greater profts, too. 4 P a g e

5 The profts wll come to very low levels but Consumers wll get benefted. However, practcally t won t happen. Wth Cole s new prce, ts sales ncrease from 20,000 KG per week to 25,000 KG per week. The reason behnd ths s the knked demand curves whch many olgopoles face n practce, whch has two parts; one an nelastc part, and the other one s elastc. In Woolworths case the demand was elastc but n Coles case t turned out to be nelastc. Wth fallng prces, greater amounts can not be bought forever. The buyng patterns wll swtch from Woolworths to Coles. However as both are close substtutes, prce changes wll result n marked reduced volume of sales, from one to the other and the total market demand for tomatoes becomes nelastc as the prce s already low. In the followng fgure of knked demand curve t can be seen that above the knk, the demand of tomatoes s elastc as Coles' prces does not changed. But below the knk, t becomes relatvely nelastc as now Coles has ntroduced a smlar reducton n prce, ultmately leadng to a prce war between the two. Thus, the best choce for both wll be to produce at pont E, as that s the knk pont at whch equlbrum occurs. 5. Concluson It can be sad that n olgopoly, the frms have ther concentraton n non compettve non prce areas; such as after-sales servce and advertsement. The frms try to make dfferentaton n ther products n the eyes of consumers, whch can be done n many ways lke makng mproved qualty products, dfferent wrappng or packagng, bonus or scheme offerngs etc. These are some deas that gve more opportuntes to each frm to be dfferent from ts rvals n terms of output and prces. The frms of olgopolstc markets may not be nterested n real competton, benefttng consumers wth lower prces. Rather, they operate n ways to mantan ther ''cosy'' share of the market and hgh levels of profts. Ths s the reason why most of the tme prces tend to stay steady n olgopoly. 6. References: Borensten, S. and Rose, N. L., 1994, Competton and prce dsperson n the US arlne ndustry, Journal of Poltcal Economy 102, Campbell R. McConnell, (1972); Economcs: prncples, problems, and polces. McGraw- Hll, 1972 Chrs Terry, Kevn Forde, (1992);Mcroeconomcs: an ntroducton for Australan students. McGraw-Hll, 1992 Fgure 1: Knked demand curve Woolworths knows that wth ts prce reducton, t wll make more sales, but only f prce reducton step s not taken by Coles n response. If Coles does and f Woolworths also cut ts prce even further, n overall no more profts wll be ganed by ether of both. Edward C Rosenthal, (2011);The Complete Idot's Gude to Game Theory. Apha,2011 Gallego, G. and van Ryzn, G., 1994, Optmal dynaml prcng of nventores wth stochastc demand over fnte horzons, Management Scence 40, 999,1020. M. Shubk, "Game Theory: Economc Applcatons", Internatonal Encyclopeda of 5 P a g e

6 the Socal Scences, Macmllan Co. and The Free Press, 1968 M.O. Jackson, "Bayesan Implementaton", Economtrca, Vol. 59, No. 2(Mar.,1991), Steven Semeraro, 2001, Polcy studes, vewed 2001 Thomas Jefferson, 2004, The Thstle, vewed 4 july 2004 T. Qunt and M. Shubk, "A Bound on the number of Nash Equlbra n a Coordnate Game", Cowles Foundaton Dscusson Paper P a g e