lecture1 - 14.12 Game Theory Lecture Notes Introduction...

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14.12 Game Theory Lecture Notes Introduction Muhamet Yildiz (Lecture 1) Game Theory is a misnomer for Multiperson Decision Theory. It develops tools, methods, and language that allow a coherent analysis of the decision-making process when there are more than one decision-makers and each agent’s payo f possibly depends on the actions taken by the other agents. In such a decision process, since an agent’s preferences on his actions depend on which actions the other parties take, his action depends on his beliefs about what the others do. Of course, what the others do depends on their beliefs about what each agent does. In this way, a player’s action, in principle, depends on the actions available to each agent, each agent’s preferences on the outcomes, each player’s beliefs about which actions are available to each player and how each player ranks the outcomes, and further his beliefs about each player’s beliefs, ad in f nitum. Under perfect competition, there are also more than one (in fact, in f nitely many) decision makers. Yet, their decisions are assumed to be decentralized. A consumer tries to choose the best consumption bundle that he can a f ord, given the prices – without paying attention what the other consumers do. In reality, the future prices are not known. Consumers’ decisions depend on their expectations about the future prices. And the future prices depend on consumers’ decisions today. Once again, even in perfectly competitive environments, a consumer’s decisions are a f ected by their beliefs about what other consumers do – in an aggregate level. When agents think through what the other players will do, taking what the other players think about them into account, they may f ndac lea rwaytop
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1 \ 2L m R T (1 , 1) (0 , 2) (2 , 1) M (2 , 2) (1 , 1) (0 , 0) B (1 , 0) (0 , 0) ( 1 , 1) Here, Players 1 has strategies, T, M, B and Player 2 has strategies L, m, R. (They pick their strategies simultaneously.) The payo f s for players 1 and 2 are indicated by the numbers in parentheses, the f rst one for player 1 and the second one for player 2. For instance, if Player 1 plays T and Player 2 plays R, then Player 1 gets a payo f of 2 and Player 2 gets 1. Let’s assume that each player knows that these are the strategies and the payo f s, each player knows that each player knows this, each player knows that each player knows that each player knows this,. .. ad in f nitum. Now, player 1 looks at his payo f s, and realizes that, no matter what the other player plays, it is better for him to play M rather than B. That is, if 2 plays L, M gives 2 and B gives 1; if 2 plays m, M gives 1, B gives 0; and if 2 plays R, M gives 0, B gives -1. Therefore, he realizes that he should not play B. 1
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This note was uploaded on 11/28/2011 for the course ECONOMICS - taught by Professor Muhammadyildiz during the Spring '05 term at University of Massachusetts Boston.

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lecture1 - 14.12 Game Theory Lecture Notes Introduction...

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