Game Theory Module KRUGMAN'S MICROECONOMICS for AP* 29 65 Micro: Econ: Margaret Ray and David Anderson

What you will learn in this Module: How oligopoly can be analyzed using game theory. The concept of the prisoners’ dilemma. How repeated interactions among oligopolists can result in collusion in the absence of any formal agreement. The purpose of this module is to show how game theory is used to model the decisions made by oligopolists. The module also describes a situation known as the prisoners’ dilemma and strategies through which the firms can escape the outcome predicted by the dilemma.

Game Theory Game Theory: study of how interdependent decision makers make choices. When two firms are close rivals, the choices of each affect the outcomes for each. In other words, they are mutually interdependent. For example, if a retailer like Target lowers the price of a Nintendo Wii, it expects to steal customers from a store like Best Buy. And this prompts Best Buy to match the lower price on the Wii and maybe even offer something else to entice customers away from Target.   These strategies and mutually interdependent outcomes can be studied with game theory. One simple definition of game theory.

Non-Cooperative Games Each player competes to maximize individual payoffs and ignores the effects of his/her action on the payoffs received by the rival. When two firms are close rivals, the choices of each affect the outcomes for each. In other words, they are mutually interdependent. For example, if a retailer like Target lowers the price of a Nintendo Wii, it expects to steal customers from a store like Best Buy. And this prompts Best Buy to match the lower price on the Wii and maybe even offer something else to entice customers away from Target.   These strategies and mutually interdependent outcomes can be studied with game theory. One simple definition of game theory.

Terms to Know Payoff matrix Dominant strategy Nash equilibrium The payoff matrix is a diagram showing how the payoffs to each player in a game depend on the actions of both. A dominant strategy is an action that is a player’s best action regardless of what the other player does. A Nash equilibrium occurs when the game ends, and each player is happy with the outcome, given the choice made by the rival.

Prisoner’s Dilemma The payoff matrix below summarizes the strategies and outcomes. The payoffs are measured as years in prison, so smaller numbers are preferred. Each player has an incentive to choose an action that benefits his/herself at the other player’s expense. Both players are then worse off than if they had acted cooperatively. Confession is the dominant strategy when the game is played simultaneously and they cannot talk (collude). No matter what Crook #2 does, it’s always better for Crook #1 to confess. The same is true of Crook #2’s thinking. This is the Nash equilibrium.   Characteristic of the prisoner’s dilemma is that players pursue their dominant strategy and the game comes to Nash equilibrium. However, the outcome is an undesirable one and could have been avoided through some kind of cooperative agreement (collusion). Crook 2 Confess Silent Crook 1 #1: 5 years #2: 5 years #1: 1 year #2: 20 years #1: 20 years #2: 1 year #1: 2 years #2: 2 years

Repeated Interaction and Tacit Collusion Repeated interaction can lead to strategic behavior Tit for tat strategy Tacit Collusion Strategic Behavior: taking account of the effects of an action today on the future actions of other players in the game. One renowned strategy in game theory is one called “tit for tat”. The strategy is very simple. The firm begins by cooperating today. Then every day from this point forward, the firm will do today, whatever the other firm did yesterday. Tacit Collusion: cooperation among producers, without a formal agreement, to limit production and raise prices so as to raise profits.