lecture 5 - 1 LECTURE 5 GAME THEORY 2 Whats Game Theory?...

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Unformatted text preview: 1 LECTURE 5 GAME THEORY 2 Whats Game Theory? Game Theory allows us to describe and analyze social and economic situations as if they were games of strategy. A Game is an abstract set of rules that constraints the behavior of players and defines outcomes on the basis of the actions taken by the players. Players : each can choose from a set of available actions Payoff : depends on each players own choice of strategies and the choices of strategies of other players Rules of Game : timing to action; information available at the time a strategy choice needs to be make; what are regarded as admissible strategies; cooperation allowed? etc. ) 3 How to Describe A Game? Normal Form/Strategic Form: Payoff matrices Extensive Form: Game tree Example 7.1: OS Game between IBM and Toshiba Players: IBM and Toshiba Payoff: Compatibility would be beneficial to both. However, IBM would prefer to use DOS and Toshiba would prefer to use UNIX. Rules: Using DOS or UNIX; IBM moves first; perfect information. 4 How to Describe A Game? Example 7.1 (a) Perfect information: Toshiba knows what IBM chooses when it makes its decisionextension form. 5 How to Describe A Game? Example 7.1 (a) Perfect information: Toshiba knows what IBM chooses when it makes its decisionnormal form. Using a payoff matrix to describe the payoffs to all players resulted from each strategy of each player. Strategy: a complete plan of action for the player that tells us what choice he should make at any node of the game tree or in any situation that might arise during the play of the game. In this example, we have: IBMs strategy: DOS or UNIX; Toshibas strategy: (DOS|DOS, DOS|UNIX), (DOS|DOS, UNIX|UNIX), (UNIX|DOS, DOS|UNIX), (UNIX|DOS, UNIX|UNIX) 6 How to Describe A Game? Example 7.1 (a) Perfect information: Toshiba knows what IBM chooses when it makes its decisionnormal form. Toshiba (DOS | DOS, DOS | UNIX) (DOS | DOS, UNIX | UNIX) (UNIX | DOS, UNIX | UNIX) (UNIX | DOS, DOS | UNIX) DOS 600, 200 600, 200 100, 100 100, 100 IBM UNIX 100, 100 200, 600 200, 600 100, 100 7 How to Describe A Game? Game of Perfect Information : the players know everything that happened in the game up to the point when their turn to move occurs and they must make a decision. In other words, each node of the game tree is distinguishable to the player moving there. Game of Imperfect Information : the player does not know all the choices of the other player who preceded her when she reaches a decision point. 8 How to Describe A Game? Example 7.1 (b) Imperfect information: Toshiba does not know what IBM chooses when it makes its decision extension form. 9 How to Describe A Game?...
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This note was uploaded on 01/17/2009 for the course ECON ECON 191 taught by Professor Chan during the Spring '09 term at HKUST.

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lecture 5 - 1 LECTURE 5 GAME THEORY 2 Whats Game Theory?...

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