Lecture 8: Oligopoly

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1 Lecture 8: Oligopoly Oligopoly and Game Theory In Perfect Competitive markets and Monopoly, producers can not easily change the market s conditions. In oligopoly the decisions of participants producers have a strategic view. The producer can decide for issues related to quantity, price and the decisions of other producers. Strategic attitude can be better studied in the context of game theory. In microeconomics game theory has substantial meaning.

2 The main parameters of a game and the Predominant Strategies A game is a deductive view of reality. The main principles of a game are the following: Players: The players may be individuals or institutions. Games rules: They determine the framework of players moves. Players strategies: It s a plan, which determines the player s moves during the game. Players choices: It refers to the decisions, the player makes according to his strategy. Players returns: The player s substantial or moral satisfactory after the game is ended.

3 Table 1

4 Player s A strategy is either up or down. Player s B strategy is either left or right. The incentives of this game lead player A to choose Down and player B to choose Left. The number of all strategies is not tantamount. There are predominant strategies, which the players want to follow and may follow to equivalence, but this is not sure. In case there is not predominant strategy, the moves of one player are dependent on the moves of the other. Game for War and Peace.

5 Table 2

6 Table 3

7 Prisoners Dilemma and Nash Equivalence The equivalence of the game may be achieved even in case the players do not have predominant strategies. For such case the prisoners dilemma is of substantial importance. According to this game each prisoner has two possibilities either to confess or not to confess. The strategic no confess is predominant for both prisoner A and B separately. These are the optimal choices for both prisoners, but this is not necessary in order to achieve Nash equivalence. The choice not confess for both players will never be the optimal choice. Both players will choose confess, even if is not the optimal choice.

8 Table 4

9 Table 5

10 The existence of high price will lead each firm to produce less than it would happen. Legal reasons. The alteration of prisoner s dilemma. Each firm has the incentive not to abide the agreement. The Nash equivalence will be for both players abide the agreement.

11 The strategic choice of quantity and the Cournot Model The firms do not come in touch for the level of quantity. Each one reacts to the supply choices of the other. C=c*Qi MC is the same for both firms. P(Q) = A b*q Q = Q1 + Q2 Πi = P*Qi c*qi, i = 1,2. Q1 = (A b*q2 c) / 2*b Q1 = R(Q2) This is the reaction function and shows the optimal level for supply of 1, given the supply of 2.

12 Q2 = R(Q1) Q2 = (A b*q1 c) / 2*b In case Q2 = 0 => Q1 = (A c) / 2*b In case Q1 = 0 => Q2 = (A c) / b For function Q1 = R(Q2) => (maxq1, maxq2) = [(A c) / 2*b, (A c) / b)]. The edges of reaction function of firm 1 are: (Q1, Q2) = [(A c) / 2*b, 0) and (Q1, Q2) = ( 0, Q2 = (A c) / b) For function Q2 = R(Q1) => (maxq1, maxq2) = [(A c) / b, (A c) /2* b)]. The edges of reaction function of firm 2 are: (Q1, Q2) = [(A c) / b, 0) and (Q1, Q2) = ( 0, Q2 = (A c) /2* b)

13 Diagram 1

14 Cournot Nash equivalence The two functions are linked at point A (Q1*, Q2*). There is the Nash equivalence. In any other quantity point (Q) there is not equivalence. The only possible choice is Q1=Q1* and Q2=Q2* The optimal quantities are not necessarily the same in the Nash Cournot equivalence, but are dependent on the form of the demand and cost functions of each firm. The strategic choice of price and the Bertrand Model The strategic variable in Bertrand s model is the price and not the quantity. Π1 = pi * D(p1, p2) c* D(p1, p2), i = 1,2

15 D(p1,p2) = D(p1) if p1<p2, D(p1,p2) = ½ * D(p1) if p1= p2 and D(p1,p2) = 0 if p1> p2. Assuming that p1*>p2*>c => The firm 1 will have zero demand. Assuming that p1*=p2*-e, e>0 => The firm 1 will obtain all the demand of the market. The process will keep existing till the point where p1*=p2*=c. The reduction of prices will not continue under the level of marginal cost. This exists in the case of perfect competitive market. This is called Bertrand pardox.

16 Comparison between Oligopoly, Monopoly and Perfect Competitive Markets Monopoly: Qm = (A-c) / 2*b. Cournot Model: Q(Cournot) = 2*(A-c)/ 3 * b. Perfect Competitive Market: Q(comp) = (A c) / b Compared these three markets there exists: Qm < Q(Cournot) < Q(comp) = > ½ < 2/3 > 1.