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Oligopoly Dr. Jennifer P. Wissink ©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved. Oligopoly (Competition Among A Few): Structure In an oligopoly there are very few sellers of the good. The product may be differentiated among the sellers (e.g. automobiles) or homogeneous (e.g. gasoline). Entry is often limited either by legal restrictions (e.g. banking in most of the world) or by a very large minimum efficient scale (e.g. overnight mail service) or by strategic behavior. Sill assuming complete and full information. Oligopoly: Conduct Harder to model! (Compared to perfect competition and monopoly and monopolistic competition.) In an oligopoly – firms know that there are only a few large competitors. – competitors take account of the effects of their actions on the market. To predict the outcome of such a market, economists frequently use game theory methods. Game Theory: Setup List of players: all the players are specified in advance. List of actions: all the actions each player can take are spelled out. Rules of play: who moves and when is spelled out. Information structure: who knows what and when is spelled out. Strategies: the set of actions players can use. Payoffs: the amount each player gets for every possible combination of the players’ strategies. Solution or equilibrium concept: a way you reason that players select strategies to play, and then consequently how you predict the outcome of the game. Solution Concept: Dominant Strategy Equilibrium A Dominant Strategy Equilibrium of a game is a set of strategies for all players, such that, for each player his payoff from playing his dominant strategy is at least as large as his payoff would be by playing any other strategy, no matter what his rivals choose as their strategies. Solution Concept: Nash Equilibrium Named after John Nash - a Nobel Prize winner in Economics. Did you see A Beautiful Mind? A Nash Non-cooperative Equilibrium of a game is a set of strategies for all players, such that, when played simultaneously, have the property that no player can improve his payoff by playing a different strategy, given the strategies the others are playing. Each player maximizes his or her payoff under the assumption that all other players will do likewise. Cournot-Nash Duopoly: A NonCooperative Outcome in Quantities Pioneered by Antoine Augustin Cournot, circa 1838. Duopoly an oligopoly of 2 firms. Firms selling identical spring water. Firms have identical cost functions. Firms decide how many units to put on the market; q1 and q2. Market then determines the price: PD = f(Q) where Q=q1+q2. So…,GIVEN what your rival is putting on the market, the more you put on the market, the lower the price for both of you, and vice versa. Cournot-Nash Duopoly: A NonCooperative Outcome in Quantities Firm i’s strategic choice variable = qi ,that is, its output level. Firm i’s conjecture about its rival when deciding his qi is NASH – meaning firm i figures out a best reaction to firm j’s strategic choice. So, in this Cournot-Nash game you would get the following: – BRF1: Firm 1’s Best Response Function » tells what quantity firm 1 should put on the market GIVEN firm 2’s quantity. – BRF2: Firm 2’s Best Response Function » tells what quantity firm 2 should put on the market GIVEN firm 1’s quantity. Cournot-Nash Duopoly: A NonCooperative Outcome in Quantities When firm 1’s best response to firm 2 is simultaneously firm 2’s best response to firm 1, we have a Nash equilibrium in quantities: q1CN and q2CN. The full Cournot-Nash(CN) Equilibrium is then: – – – – QCN = q1CN + q2CN Get PCN from plugging QCN into demand: PD = f(QCN) Get profit for each firm: P1CN and P2CN Get joint profit: PjointCN= P1CN + P2CN Properties of the CournotNash Equilibrium for Duopoly Cournot Nash compared to simple monopoly(SM) and to perfect competition(*). Q* > QCN > QSM P* < PCN < PSM PSM > PJointCN > PJoint* Deadweight loss with CN is less than for a simple monopoly in the same market but still positive, thus greater than the deadweight loss from a competitive market. Extensions to the model? – More than two firms? Can do. – Different cost structures? Can do. Assume: PD=12-2Q, Q=q1+q2, tc1=tc2=0 mc1=mc2=0 Simple Monopolymr=12-4Q & set mr=mc, so Qsm=3, Psm=$6, Profitsm=$18 Perfect Competition Set PD=mc and so Q*=6 and P*=0, Profit =$0 $ 14 12 10 8 6 4 2 0 -2 0 -4 -6 -8 -10 Demand MC MR 1 2 3 4 5 Q 6 7 8 9 The Cournot-Nash Reaction Functions Consider firm 2’s reactions to firm 1’s quantities. Suppose q1=0. Then firm 2 would do what a monopolist would do, and q2=3. Suppose q1=6. Then firm 2 would see there was no room for it and select q2=0. Between q1=0 and q1=6, there is a “best response” from firm 2’s point of view, which lies on the red straight line. q2 q1 Consider firm 1’s reactions to firm 2’s quantities. Suppose q2=0. Then firm 1 would do what a monopolist would do, and q1=3. Suppose q2=6. Then firm 1 would see there was no room for it and select q1=0. Between q2=0 and q2=6, there is a “best response” from firm 1’s point of view, which lies on the blue straight line. The Cournot-Nash equilibrium is where the blue and red intersect at q1=q2=2. So, QCN=4 and PCN=$4. Each firm gets profit=$8. Joint profit = $16. Demand Demand MC MR $ 14 12 10 8 6 4 2 P*= 0 -2 0 -4 -6 -8 -10 1 2 3 4 5 6 7 Marginal revenue Q 8 9 Bertrand-Nash Duopoly: An Alternative Non-cooperative Outcome Pioneered by Joseph Louis Francois Bertrand, circa 1883. Duopoly an oligopoly of 2 firms. Firms selling identical spring water. Firms have identical cost functions. Firms decided what price to post on the market. What each firm sells depends on their own price along with their rival’s price: q1D = g(P1 , P2) and q2D = h(P1 , P2) If P1 < P2 everyone buys from firm 1 If P1 > P2 everyone buys from firm 2 Bertrand-Nash Duopoly: A Non-cooperative Outcome Firm i’s strategic choice variable = Pi Firm i’s conjecture about rival when deciding his Pi is NASH – meaning firm i figures out a best reaction to firm j’s strategic choice So, in this Bertrand-Nash game you would get the following: – BRF1: Firm 1’s Best Response Function » tells what price firm 1 should choose GIVEN firm 2’s price – BRF2: Firm 2’s Best Response Function » tells what price firm 2 should choose GIVEN firm 1’s price Bertrand-Nash Duopoly: A Non-cooperative Outcome When firm 1’s best response to firm 2 is simultaneously firm 2’s best response to firm 1, we have a Nash equilibrium in prices: P1BN and P2BN The full Bertrand-Nash(BN) Equilibrium is then: – PBN = P1BN = P2BN – Firm 1 and Firm 2 split the market in any way provided that: q1BN + q2BN = QD(PBN) – Get profit for each firm: P1BN and P2BN – Get joint profit: PjointBN = P1BN + P2BN Properties of the BertrandNash Equilibrium for Duopoly Bertrand-Nash Equilibrium compared to simple monopoly and to perfect competition Q* = QBN > QSM P* = PBN < PSM PSM > PJointBN = PJoint* Deadweight loss with BN is zero! Bertrand all you need is one competitor to get competitive results!! Extensions to the model? Duopoly Results as N Changes Bertrand compared to Cournot. – When N=1 then Cournot = Bertrand = Simple Monopoly – When N>1 then... » Bertrand=Perfect Competition » Cournot is in between Perfect Competition and Monopoly – When N gets large enough, then... » Cournot = Bertrand =Perfect Competition Results have different implications for anti-trust action. – Should Coke be allowed to merge with Dr. Pepper? Should Pepsi be allowed to merge with 7-Up? Good questions. – Should Chrysler be allowed to merge with Fiat? – How about GE being able to sell NBC Universal to Comcast? – How about US Airways and United? Edward Chamberlin: A Cooperative Oligopoly Outcome (Collusion) circa 1930’s The duopolists can do better than the Nash Non-Cooperative Equilibrium – Bertrand or Cournot. So far, because the equilibrium is non-cooperative, we have ruled out the possibility of collusion between the two firms. Collusion means that the firms explicitly and/or implicitly cooperate in choosing a market output and the division of output between them. (Note, if they set the output level, then the market sets the price.) If the duopolists collude and divide up the market privately, they can produce the monopoly quantity and divide the monopoly economic profits. Since the monopoly economic profits are more than the sum of the duopoly profits, the duopolists are better off if they collude. When we allow the possibility of collusion the game can turn out differently. No longer a NONcooperative game. Chamberlinian Collusion With A Duopolymimic a multi-plant monopoly With only a couple/few identical firms, and homogeneous output, this might be expected. Cournot-Nash Joint Profit V1 V2 However, when firms have different cost structures… X1 Cournot-Nash Joint Profit X2 X1=6, X2=4, sum=10 V1=5, V2=5, sum=10 “Collusive Monopoly” Joint Profit W1=11, W2=11, sum=22 W1 W2 “Collusive Monopoly” Joint Profit Y1 Y2 Y1=19, Y2=3, sum=22
