Game theory in Oligopoly

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  • 1. IJASCSE, Vol 1 Issue 2, 2012 Sep. 30 Game theory in Oligopoly Prof. Marx Boopathi, Nikolaj Sujen. transforming marketplace, game theory is theAbstract kernel of a new economics.The game theory techniques are used to find 2. The Oligopolythe equilibrium of a market. Game theoryrefers to the ways in which strategic The main characteristics of an oligopolyinteractions among economic agents market are:produce outcomes with respect tothe preferences (or utilities) of those agents, o There are few firms to competewhere the outcomes in question might have in. It may happen that a largebeen intended by none of the agents. The number of firms are there butoligopolistic market structures are taken andhow game theory applies to them is two very big manufacturersexplained. dominate the industry.Keywords: game theory, oligopoly, market o The Concentration Ratio of thestructure market sales is in the hand of those two producers. If they account for 90% ratio of share 1. Introduction of market sales in the industry itThe market structure identifies how a market is called a 2 firm concentrationworks in terms of the number of the firms ratio of 90%. The airlinesengaged in, the nature of the produced industry is a good example of it.product, efficiency of firm etc. There are o The larger of the two firms hasmany forms of market structure and the most Price leadership that is followedrevealed is Oligopoly. In oligopolistic markets,there always remain a struggle between self by smaller firminterest and cooperation. If the output is o Collusion Potentiallimited by all the firms, the price becomes o Interdependence betweenhigh, but it implies that then output will be firms—Behaviour is affected byexpanded because of firm’s incentive to do actions of rivalsthat. o Goods manufactured may be either highly differentiated orThe analysis through Game theory is directlyrelevant to the behaviour of businesses in homogeneousoligopolistic markets. The decisions taken o loyalty against brand & brandingusing the theory about the self interest and may cause a potential source ofcooperation decide the investment and advantagespending of the firms. Conventional o Cournot Model suggesteconomics describes the operation of mature equilibrium in long run cause& established markets, but it throws no lighton people’s creativity in finding new ways of normal profits and equal marketinteracting with one another. The economics shareof markets is dynamic and evolving. o Use of game theory to explain behaviour of the firms to aThe innovation continues and nothing is extenttaken given. In the rapidly and free-form 1|Page
  • 2. IJASCSE, Vol 1 Issue 2, 2012 Sep. 30 o AC curve is saucer shaped – The fundamental assumption of the game theory is that all players are intelligent and minimum efficiency may be rational and each player uses those needed to cover large range of strategies which result in the long run output equilibrium. At this point not anyone wants to o Entry restricted due to high withdraw from its strategic ideology. barriers In the grocery market’s duopolistic o Examples include Moody’s & competition, like in the Australian case, the S&P in the ratings market, Coca game theory is particularly important as it cola and Pepsi, Visa and offers Low barriers to entry without any license, any upfront cost or any infrastructure. Master card etc. Because of the already present two big bulls, most retailers avoid entering into market 3. Game theory because they can not afford.“It is a universal language for the unification 3.1 Nash Equilibriumof the behavioural sciences.” Gintis(2000, 2009). In the supermarkets duopolistic competition, like in the Australian case, the strategiesIn simple words this theory studies peoples’ adopted are related to EDLP (everyday lowbehaviour in strategic situations. It is the pricing) and HLP (high low pricing) thatformal study of cooperation and conflict and change from week to week. Both strategiescan be applied where the actions of several are dominant for maximising sales and profitsfirms are interdependent. The game theory with focus on week to week sales. Theconcepts provide a language to structure, strategy related to HLP is more transparentformulate, analyze and understand strategic and explicit, which consists of in storescenarios. advertising, media advertising, merchandising and price reductions. This strategy in gameEdward C Rosenthal, (2011, p.18) states that theory is shown in the following table. As per“Game Theory is the study of the ways in the game theory it is a normal game betweenwhich strategic interactions among rational the two players.players produce outcomes with respect to thepreferences of those players, none of whichmight have been intended by any of them.”In a duopoly or the oligopolistic market, eachfirms’ profits depend on other firms’ actionsresulting in the "prisoners’ dilemma". Theprisoners dilemma is a particular game, Source: An application of Game theorywhich illustrates the difficulty of cooperation,even when it is in the best interests to market The parameters in above table can take anyplayers. The self owned dominant strategies values but the constraint is that each playerare selected by the both market players for has played the game several times andtheir short-sighted personal profits. knows other players components of strategyEventually, equilibrium is reached where both which may be different. That means eachmay worse off than they would have been, if player has in all nine strategies and each playan alternative (non-dominant) strategy could requires three strategies at one time. Thus inhave been agreed upon between them. all there are twenty seven pay offs for this 2|Page
  • 3. IJASCSE, Vol 1 Issue 2, 2012 Sep. 30 there and the quantity would also be socially efficient. M. Shubik, (1968,p.) claims thatgame. This implies that it would not be easyto achieve Nash equilibrium but not The Nash equilibrium in the general gameimpossible. does not yield a higher payoff, given the other players chosen strategies. It is a notion ofThe sales being observed on weekly basis, if joint rationality as each player best respondsthese are in line with expectations and long to the other players.run objectives of player one and if rivals arefollowing passive strategies then the 3.2 Bertrand Equilibriumprobability that player two too will continuethe passive strategy is quite high and vice For differentiated products, two identical firmsversa. The same strategy is applied for choose prices simultaneously and end upaggressive strategies also. However, within with the situation likely to perfect competition.this game the costs are likely to remain lowand profits may soar. The only pure-strategy Nash equilibrium is p1* = p2* = c because the best response is playedIn practice, however it does not happen and by both firms to each otherrivals may adopt an alternate strategy to bebetter off. The following table shows the pay Neither firm has an incentive to deviate tooff matrix for nine of twenty seven strategies some other strategy.that are implicit in the above table. If p1 and p2 > c, a firm could gain by undercutting the price of the other and capturing all the market. If p1 and p2 < c, profit would be negative To hack with quantity and profits, if both firms compete viciously on price then equilibrium will occur only where price equals the marginal cost. This is because both firms areSource: An application of Game theory producing identical products and if one reduces its price the other will not be leftThe each cell in the above table is showing behind and try to cut its price still lower.the pay off for each player for all the three However this equilibrium is socially efficientdifferent strategies. The Nash equilibrium is as consumers will be benefitted most.also shown but this level also can’t beconsidered as a stable equilibrium because it 3.3 Cournot Equilibriumis attributed to higher inventory andpromotional costs. If both firms become price takers and put the price as secondary option and considerIf instead of two, there are more firms in the quantity produced they can achieve Cournotmarket, the price effect will be smaller equilibrium by applying game theory. As theresulting in the lower Nash equilibrium price. product is identical profit maximisation usingIf the number of firms reaches infinity, the quantity for one firm depends on the quantityprice effect will also approach zero. So, produced by the other one. In this modeloutput will be increased by each sellerwhenever the price moves above MC. In theend, the perfectly competitive price will be 3|Page
  • 4. IJASCSE, Vol 1 Issue 2, 2012 Sep. 30 Australia. In a study of retail marketing Bovil (2008) stated that “When you have that much (market share) you create market distortion - • firms set quantities rather than prices a supplier who has to deal with someone with and each firm’s own decisions are that much power works from a weak position. recognised about qi affect price Two retailers dominating sales did not qualify – P/qi  0 as a "market" under economic definitions.” • However, each firm thinks that any In an oligopolistic market competition is other firm is not affected by its intense. Both non-price and price techniques decisions are used to compete. The warranties and – qj /qi = 0 for all j i tricky advertisements are common aspect. As • For profit maximization, the FOC are per an article in weekly times, marketing  i  PQ   P Q qi  C i (qi )  0 manager, Woolworths (2001), qi We will not be beaten on price. If our • The firm maximizes profit where MRi = competitor is selling item X for less, we will MCi match their prices, whether the items price • Price exceeds marginal cost byP Q q i has been reduced for a special sale or not. We will replace the item without cost if it isIf q1 is the qty produced by one firm and q2 is found to be defective in any way.the qty produced by other firm, then the totalqty produced will be q=q1+q2. Using game In particular, Woolworths has succeeded withtheory, the solution will be its Were the fresh food people advertising campaign.q1=q2= (a-cb)/3, where c is the MC of thefirm In oligopoly mutually interdependence is a must. If policy of price change is adopted byIt can be noted that this equilibrium is in one, then this will affect the sales of other firmbetween monopoly and oligopoly production in the market. This can be understood aslevels and the profit margins earned by the follows.two firms are less than half of those asearned by the monopolist. Suppose Coles and Woolworths initially sell tomatoes @ $6 per KG. Woolworths lowers 4. An example its 2price by $1 per KG so that its sales rise from 10,000 KG per week to 20,000 KG perFor example, a few, large firms dominate week. This implies that at this stage demandmany Australian markets. A duopoly exists in curve is elastic for tomatoes; the 17%the grocery market of Australia, where it is decrease in price has resulted in 50%dominated by Coles and Woolworths, increase in volume of sales. So, as Colesnationally. Both of these have extensive and begins to lose its sales to Woolworths, towide distribution systems, with many stores in match Woolworths price, it also reduces pricealmost all in regional and urban areas across by $1 per KG.Australia. Other firms, if they wish to enterneed a large investment to compete with Coles does not stop here and decides to gothese. further by reducing its prices to $3 per KG. The reason provided that when WoolworthsIn the grocery market of Australia, the seller decreased its price, it made less profit perconcentration ratio is approx 80%; the two kilogram, but as many more kilograms oflargest firms Coles and Woolworths account tomatoes were sold, overall it made greaterfor 80% of total sales of groceries in profits. If Coles do the same, it will end up making greater profits, too. 4|Page
  • 5. IJASCSE, Vol 1 Issue 2, 2012 Sep. 30 The profits will come to very low levels but Consumers will get benefited.However, practically it won’t happen. With 5. ConclusionCole’s new price, its sales increase from20,000 KG per week to 25,000 KG per week. It can be said that in oligopoly, the firms have their concentration in non competitive nonThe reason behind this is the kinked demand price areas; such as after-sales service andcurves which many oligopolies face in advertisement. The firms try to makepractice, which has two parts; one an differentiation in their products in the eyes ofinelastic part, and the other one is elastic. consumers, which can be done in many ways like making improved quality products,In Woolworths case the demand was elastic different wrapping or packaging, bonus orbut in Coles case it turned out to be inelastic. scheme offerings etc. These are some ideasWith falling prices, greater amounts can not that give more opportunities to each firm tobe bought forever. The buying patterns will be different from its rivals in terms of outputswitch from Woolworths to Coles. However and prices. The firms of oligopolistic marketsas both are close substitutes, price changes may not be interested in real competition,will result in marked reduced volume of sales, benefitting consumers with lower prices.from one to the other and the total market Rather, they operate in ways to maintain theirdemand for tomatoes becomes inelastic as cosy share of the market and high levels ofthe price is already low. profits. This is the reason why most of the time prices tend to stay steady in oligopoly.In the following figure of kinked demandcurve it can be seen that above the kink, the 6. References:demand of tomatoes is elastic as Colesprices does not changed. But below the kink, Borenstein, S. and Rose, N. L., 1994,it becomes relatively inelastic as now Coles Competition and price dispersion in the UShas introduced a similar reduction in price, airline industry, Journal of Political Economyultimately leading to a price war between the 102, 653-683.two. Thus, the best choice for both will be toproduce at point E, as that is the kink point at Campbell R. McConnell, (1972); Economics:which equilibrium occurs. principles, problems, and policies. McGraw- Hill, 1972 Chris Terry, Kevin Forde, (1992);Microeconomics: an introduction for Australian students. McGraw-Hill, 1992 Edward C Rosenthal, (2011);The Complete Idiots Guide to Game Theory. Apha,2011 Figure 1: Kinked demand curve Gallego, G. and van Ryzin, G., 1994, Optimal dynamil pricing of inventories with stochasticWoolworths knows that with its price demand over finite horizons, Managementreduction, it will make more sales, but only ifprice reduction step is not taken by Coles in Science 40, 999,1020.response. If Coles does and if Woolworthsalso cut its price even further, in overall nomore profits will be gained by either of both. M. Shubik, "Game Theory: Economic Applications", International Encyclopedia of 5|Page
  • 6. IJASCSE, Vol 1 Issue 2, 2012 Sep. 30the Social Sciences, Macmillan Co. and TheFree Press, 1968M.O. Jackson, "Bayesian Implementation",Economitrica, Vol. 59, No. 2(Mar. ,1991),461-477.Steven Semeraro, 2001, Policy studies,viewed 2001Thomas Jefferson, 2004, The Thistle, viewed4 july 2004T. Quint and M. Shubik, "A Bound on thenumber of Nash Equilibria in a CoordinateGame", Cowles Foundation Discussion Paper1095. 6|Page