Ch.14 Notes

# Ch.14 Notes - Intermediate Microeconomics Professor Yongmin...

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Intermediate Microeconomics Professor Yongmin Chen Topic 10. Game Theory and Strategic Behavior Game Theory: An Introduction In oligopoly markets firms interact with each other when making decisions. The study of strategic interactions between firms is a subject of game theory. A major development of microeconomics in the last decade is in game theory and its application to understanding the strategic interactions on the oligopoly markets. A game is a decision situation where more than one decision agent is involved. A participant of the game (a firm, a consumer, government, etc) is called a player. Each player may only undertake certain actions. Depending on the actions of all players, each player receives a payoff from the game (that is why each player needs to think about the actions of other players before he chooses an action). Example 10-1. A bidding game. (To be explained in class. All of you and I are players) To simplify analysis, we will focus on situations where there are only two players. Let's call these two players A and B. A strategy of a player is a plan by this player on what actions to take. A pair of strategies is said to be a Nash equilibrium if each player's strategy is optimal given the strategy of the other player. In other words, a Nash equilibrium is a situation where no player can unilaterally improve his (her) payoff.

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Example 10-2. The Prisoner's Dilemma . Two suspects are arrested and charged with a crime. The police lack sufficient evidence to convict the suspects unless at least one confesses. The two suspects are held at two separate cells and can choose either to confess or to deny. If one confesses but the other dos not, then the one confessed will be set free immediately (payoff = 0) and the one not confessed will receive 5-year sentence (payoff = -10); if both confess, then both will be sentenced to 4 years in prison (each has payoff = -4); if neither confesses, both will be convicted a minor offense and receive 3-month sentence (payoff = -1). What are the strategies of each suspect? What are the Nash equilibria of this game? The strategies of each player are: confess, and deny. The only Nash equilibrium is (confess, confess). To see this pair of strategies constitute a Nash equilibrium, we need to check that given the other player is confessing, a player does best by confessing too. To see that there are no other Nash equilibrium, we need to check that at any other pair of strategies, at least one player can benefit by deviating to confessing.
Example 10-3. The battle of the sexes. A young couple need to decide what to do for an evening. They both want to spend the evening together, but the husband prefers to watch a boxing game, while the wife prefers to watch a movie. The game is described as follows: What are the strategies of the husband and the wife? What are the Nash equilibria of the game? Each has two

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## This note was uploaded on 03/31/2008 for the course ECON 3070 taught by Professor Loh,joyce during the Spring '07 term at Colorado.

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Ch.14 Notes - Intermediate Microeconomics Professor Yongmin...

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