Managerial Economics ECO404 OLIGOPOLY: GAME THEORETIC APPROACH

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1 OLIGOPOLY: GAME THEORETIC APPROACH Lesson 31 OLIGOPOLY: GAME THEORETIC APPROACH When just a few large firms dominate a market so that actions of each one have an important impact on the others. In such a market, each firm recognizes its strategic interdependence with others. An oligopoly is a market dominated by a small number of strategically interdependent firms. Oligopoly presents the greatest challenge to economists. The essence of oligopoly is strategic interdependence. The economists have had to modify the tools used to analyze other market structures and to develop entirely new tools as well. One approach game theory has yielded rich insights into oligopoly behavior. Economists have developed: Collusive Models Limit-Pricing Models Managerial Models Behavioral Models But these models do not provide a general theory of oligopoly in the sense that none of these models could fully explain the decision-making process of oligopolists. GAME THEORY: is concerned with the choice of the best or optimal strategy in conflict situation. The lessons drawn from homely games like chess and poker had nearly universal application to economic situations in which the participants had the power to anticipate and affect other participants' actions. While John von Neumann and Oskar Morgenstern did pioneering work in this field as early as the late 1940s, the analytical breakthrough was made by John Harsanvi, John Nash and Reinhard Selton, who were awarded Nobel Prize (in 1994) "for their pioneering analysis of equilibrium in the theory of non-cooperative games." The Nobel prize (2005) was awarded to: Robert J. Aumann and Thomas C. Schelling "for having enhanced our understanding of conflict and cooperation through game-theory analysis". John Nash introduced the distinction between cooperative games, in which binding agreements can be made, and non-cooperative games, where binding agreements are not feasible. Nash also developed an equilibrium concept for predicting the outcome of non-cooperative games that is called Nash equilibrium. GAME THEORY BASICS Types of Games Zero-sum game: offsetting gains/losses. Positive sum game: potential for mutual gain. Negative-sum game: potential for mutual loss. Cooperative games: joint action is favored. Non-Cooperative Games Role of Interdependence Sequential games involve successive moves. Simultaneous-move games incorporate coincident moves. Game theory approach An approach to modeling strategic interaction of oligopolists in terms of moves and countermoves Copyright Virtual University of Pakistan 1

2 GAME THEORY: ELEMENTS Strategies: A Strategy is a specific course of action with clearly defined values for policy variables. A strategy is dominant if it is optimal regardless of what the other player does. Payoff of a strategy is the net gain it will bring to the firm for any given counter-strategy of the rival firm Payoff matrix is the table giving the payoffs from all the strategies open to the firm and the rivals responses Policy Variables: Price, Quantity, Quality, advertising Research and Development Expenditure, Changes in the number of products. Players: players are interdependent Players are the decision-makers (the managers of oligopolist firms). other players actions are not entirely predictable GAME THEORY concepts are used to develop effective competitive strategies for setting prices, the level of product quality, research and development, advertising, and other forms of non price competition in oligopoly markets. STRATEGIC BEHAVIOR refers to the plan of action or behavior of an oligopolist, after taking into consideration all possible reactions of its competitors, as they compete for profits or other advantages. Since there are only a few firms in the industry, the actions of each affects the others, and the reaction of the others must be kept in mind by the first in charting its best course of action. Thus, each oligopolist changes the product price, the quantity of the product that it sells, the level of advertising, and so on, so as to maximize its profits after having considered all possible reactions of its competitors to each of its courses of action. Every game theory model includes players, strategies, and payoffs. The players are the decision makers (here, the managers of oligopolist firms) whose behavior we are trying to explain and predict. The strategies are the choices to change price, develop new products, undertake a new advertising campaign, build new capacity, and all other such actions that affect the sales and profitability of the firm and its rivals. The payoff is the outcome or consequence of each strategy. For each strategy adopted by a firm, there is usually a number of strategies (reactions) available to a rival firm. The payoff is the outcome or consequence of each combination of strategies by the two firms. The payoff is usually expressed in terms of the profits or losses of the firm that we are examining as a result of the firm's strategies and the rivals responses. The table giving the payoffs from all the strategies open to the firm and the rivals responses is called the payoff matrix. In a simultaneous-move game, each decision maker makes choices without specific knowledge of competitor counter moves. In a sequential-move game, decision makers make their move after observing competitor moves. If two firms set prices without knowledge of each other s decisions, it is a simultaneous-move game. If one firm sets its price only after observing its rival s price, the firm is said to be involved in a sequential-move game. In a one shot game, the underlying interaction between competitors occurs only once; in a repeat game, there is an ongoing interaction between competitors. A game theory strategy is a decision rule that describes the action taken by a decision maker at any point in time. A simple introduction to game theory strategy is provided by perhaps the most famous of all simultaneous-move one-shot games: The so-called Prisoner s Dilemma. PRISONERS DILEMMA The prisoner's dilemma is a fundamental problem in game theory that demonstrates why two people might not cooperate even if it is in both their best interests to do so. It was originally Copyright Virtual University of Pakistan 2

3 framed by Merrill Flood and Melvin Dresher working at RAND in Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner's dilemma" name (Poundstone, 1992). A CLASSIC EXAMPLE OF THE PRISONER'S DILEMMA IS PRESENTED AS FOLLOWS: Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only 1 year in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act? TABLE 1 PAYOFF MATRIX Individual A Individual B Confess Don't Confess Confess (5, 5) (0, 10) Don't Confess (10, 0) (1, 1) TABLE 2 DOMINANT STRATEGY Both Individuals Confess (Nash Equilibrium) Individual A Individual B Confess Don't Confess Confess (5, 5) (0, 10) Don't Confess (10, 0) (1, 1) If we assume that each player cares only about minimizing his or her own time in jail, then the prisoner's dilemma forms a non-zero-sum game in which two players may each either cooperate with or defect from (betray) the other player. In this game, as in most game theory, the only concern of each individual player (prisoner) is maximizing his or her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto suboptimal solution, that is, rational choice leads the two players to both play defects, even though each player's individual reward would be greater if they both played cooperatively. In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal. Copyright Virtual University of Pakistan 3

4 Oligopolistic firms often face a problem called the prisoners dilemma. This refers to a situation in which each firm adopts its dominant strategy but each could do better (i.e., earn larger profits) by cooperating. From Table1, we see that confessing is the best or dominant strategy for suspect A no matter what suspect B does. The reason is that if suspect B confesses, suspect A receives a 5-year sentence if he confesses and a 10-year jail sentence if he does not: Similarly, if suspect B does not confess, suspect A goes free if he confesses and receives a 10-year jail sentence if he does not. Thus, the dominant strategy for suspect A is to confess. Confessing is also the best or dominant strategy for suspect B. The reason is that if suspect A confesses, suspect B gets a 5- year jail sentence if he also confesses and a 10-year jail sentence if he does not. Similarly, if suspect A does not confess, suspect B goes free if he confesses and gets 1 year if he does not. Thus, the dominant strategy for suspect B is also to confess. From Table 2, we see that with each suspect adopting his dominant strategy of confessing, each end up receiving a 5-year jail Sentence. PRICE COMPETITION AND THE PRISONERS' DILEMMA The concept of the prisoners' dilemma can be used to analyze price and non-price competition in oligopolistic markets, as well as the incentive to cheat (i.e., the tendency to secretly cut price or sell more than its allocated quota) in a cartel. Oligopolistic price competition in the presence of the prisoners' dilemma can be examined with the payoff matrix in Table 3. The payoff matrix of Table 3 shows that if firm B charged a low price (say, $6), firm A would earn a profit of 2 if it also charged the low price ($6) and 1 if it charged a high price (say, $8). Similarly, if firm B charged a high price ($8), firm A, would earn a profit of 5 if it charged the low price and 3 if it charged the high price. Thus, firm A should adopt its dominant strategy of charging the low price. Turning to firm B, we see that if firm A charged the low price, firm B would earn a profit of 2 if it charged the low price and 1 if it charged the high price. Similarly, if firm A charged the high price, firm B would earn a profit of 5 if it charged the low price and 3 if it charged the high price. Thus, firm B should also adopt its dominant strategy of charging the low price. However, both firms could do better (i.e., earn the higher profit of 3) if they cooperated and both charged the high price (the bottom right cell). Thus, the firms are in a prisoners' dilemma: Each firm will charge the low price and earn a smaller profit because if it charges the higher price, it cannot trust its rival to also charge the high price. NON-PRICE COMPETITION, CARTEL CHEATING, AND THE PRISONERS' DILEMMA By simply changing the heading of the columns and rows of the payoff matrix in Table 3, we can use the same payoff matrix to examine non price competition and cartel cheating. For example, if we changed the heading of "low price" to "advertise" and changed the heading of "high price" to "don't advertise" in the columns and rows of the payoff matrix of Table 3, we can use the same payoff matrix of Table 4 to analyze advertising as a form of non-price competition in the presence of the prisoners 'dilemma. We would then see that each firm would adopt its dominant strategy of advertising and (as in the case of charging a low price) would earn a profit of 2. Both firms, however, would do better by not advertising because they would then earn (as in the case of charging a high price) the higher profit of 3. Similarly, if we now changed, the heading of "low price" or "advertise' to "cheat" and the heading of "high price" or "don't advertise" to "don't cheat" in the columns and rows of the payoff matrix of Table 3, we could use the same payoffs in Table 5 to analyze the incentive for cartel members to cheat in the presence of the prisoners' dilemma. In this case, each firm adopts its dominant strategy of cheating and (as in the case of charging the low price or advertising) earns Copyright Virtual University of Pakistan 4

5 a profit of 2. But by not cheating, each member of the cartel would earn the higher profit of 3. The cartel members therefore are facing the prisoners' dilemma. TABLE 3 APPLICATION: PRICE COMPETITION Dominant Strategy: Low Price L o w P rice H ig h P rice Low Price (2, 2) (5, 1) High Price (1, 5) (3, 3) TABLE 4 APPLICATION: NONPRICE COMPETITION Dominant Strategy: Advertise A dvertise D on't A dvertise Advertise (2, 2) (5, 1) Don't Advertise (1, 5) (3, 3) TABLE 5 APPLICATION: CARTEL CHEATING Dominant Strategy: Cheat Cheat Don't Cheat Cheat (2, 2) (5, 1) Don't Cheat (1, 5) (3, 3) NASH EQUILIBRIUM: DOMINANT STRATEGY To see how players choose strategies to maximize their payoffs, we begin with the simplest type of game in an industry (duopoly).composed of two firms, firm A and firm B, and a choice of two strategies for each-advertise or don't advertise., expects to earn higher profits if it advertises than if it doesn't. But the actual level of profits of firm A depends also on whether firm B advertises or not. Thus, each strategy by firm A (i.e., advertise or don't advertise) can be associated with each of firm B's strategies (also to advertise or not to advertise). The four possible outcomes for this simple game are illustrated by the payoff matrix in Table 6. The first number of each of the four cells refers to the payoff (profit) for firm A, while the second is the payoff (profit) for firm B. From Table 6, we see that if both firms advertise, firm A will earn a profit of 4, and firm B will earn a profit of 3 (the top left cell of the payoff matrix). The bottom left cell of the payoff matrix, on the other hand, shows that if firm A doesn't advertise and firm B does, firm A will have a profit of 2, and firm B will have a profit of 5. The other payoffs in the second column of the table can be similarly interpreted. If firm B does advertise (i.e., moving down the left column of Table 6), we see that firm A will earn a profit of 4 if it also advertises and 2 if it doesn't. Thus, firm A should advertise if firm B advertises. If firm B doesn't advertise (i.e., moving down the right column in Table 6), firm A would earn a profit of 5 if it advertises and 3 if it doesn't. Thus, firm A should advertise whether firm B advertises or not. 's profits would always be greater if it advertises than if it doesn't Copyright Virtual University of Pakistan 5

6 regardless of what firm B does. We can then say that advertising is the dominant strategy for firm A. The dominant strategy is the optimal choice for a player no matter what the opponent does. The same is true for firm B. whatever firm A does (i.e., whether firm A advertises or not), it would always pay for firm B to advertise. We can see this by moving across each row of Table 6. Specifically, if firm A advertises, firm B's profit would be 3 if it advertises and 1 if it does not. Similarly, if firm A does not advertise, firm B's profit would be 5 if it advertises and 2 if it doesn't. Thus, the dominant strategy for firm B is also to advertise. In this case, both firm A and firm B have the dominant strategy of advertising, and this will, therefore, be the final equilibrium. Both firm A and firm B will advertise regardless of what the other firm does and will earn a profit of 4 and 3, NASH EQUILIBRIUM Not all games have a dominant strategy for each player. In fact, it is more likely in the real world that one or both players do not have a dominant strategy. An example of this is shown in the payoff matrix in Table 10. This is the same as the, payoff matrix in Table 6, except that the first number in the bottom tight cell was changed from 3 to 6. Now firm B has a dominant strategy, but firm A does not. The dominant strategy for firm B is to advertise whether firm A advertises or not, exactly as above, because the payoffs for firm B are the same as in Table 6., however, has no dominant strategy now. What is the optimal strategy for if chooses to advertise? If chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise. TABLE 6 D o n 't A d ve rtise (2, 5 ) (3, 2 ) What is the optimal strategy for if chooses not to advertise? If chooses to advertise, the payoff is 5. Otherwise, the payoff is 3. Again, the optimal strategy is to advertise. TABLE 7 A d ve rtis e (4, 3 ) (5, 1 ) D o n 't A d v e rtis e (2, 5 ) (3, 2 ) Regardless of what decides to do, the optimal strategy for is to advertise. The dominant strategy for is to advertise. Copyright Virtual University of Pakistan 6

7 TABLE 8 Advertise (4, 3) (5, 1) D on't A dvertise (2, 5) (3, 2) What is the optimal strategy for if chooses to advertise? If chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise. TABLE 9 Advertise (4, 3) (5, 1) D on't A dvertise (2, 5) (3, 2) What is the optimal strategy for if chooses not to advertise? If chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise. TABLE 10 Advertise (4, 3) (5, 1) D on't A dvertise (2, 5) (6, 2) Regardless of what decides to do, the optimal strategy for is to advertise. The dominant strategy for is to advertise. TABLE 11 D o n 't A d ve rtise (2, 5 ) (3, 2 ) The dominant strategy for is to advertise and the dominant strategy for is to advertise. The Nash equilibrium is for both firms to advertise. Copyright Virtual University of Pakistan 7

8 TABLE 12 Advertise (4, 3) (5, 1) D on't A dvertise (2, 5) (3, 2) What is the optimal strategy for if chooses to advertise? If chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise. TABLE 13 D o n 't A d ve rtise (2, 5 ) (6, 2 ) What is the optimal strategy for if chooses not to advertise? If chooses to advertise, the payoff is 5. Otherwise, the payoff is 6. In this case, the optimal strategy is not to advertise. TABLE 14 A d ve rtise (4, 3 ) (5, 1 ) D o n 't A d ve rtise (2, 5 ) (6, 2 ) The optimal strategy for depends on which strategy is chosen by Firms B. does not have a dominant strategy. TABLE 15 A d ve rtise (4, 3 ) (5, 1 ) D o n 't A d ve rtis e (2, 5 ) (6, 2 ) What is the optimal strategy for if chooses to advertise? If chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise. Copyright Virtual University of Pakistan 8

9 TABLE 16 D o n 't A d ve rtise (2, 5 ) (6, 2 ) What is the optimal strategy for if chooses not to advertise? If chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise. TABLE 17 D on't A dvertise (2, 5) (6, 2) Regardless of what decides to do, the optimal strategy for is to advertise. The dominant strategy for is to advertise. TABLE 18 D on't A dvertise (2, 5) (6, 2) The dominant strategy for is to advertise. If chooses to advertise, then the optimal strategy for is to advertise. The Nash equilibrium is for both firms to advertise. The Nash equilibrium is a situation where each player chooses his or her optimal strategy, given the strategy chosen by the other player. TABLE 19 D o n 't A d ve rtise (2, 5 ) (6, 2 ) Copyright Virtual University of Pakistan 9