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Section-6-Game-Theory-Dominant-Strategies-slides

Section-6-Game-Theory-Dominant-Strategies-slides - Game...

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Game Theory: Dominant and Dominated Strategies Todd Sarver Northwestern University Econ 310-2 – Fall 2011 Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 1 / 30
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Outline 1 Components of a Game 2 Examples 3 Solution Concepts Dominant Strategies Iterated Elimination of Strictly Dominated Strategies 4 Non-Dominance Solvable Games 5 Pareto Efficiency Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 2 / 30
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Components of a Game Definition A Game consists of: 1 A set of players: 1 , . . . , n 2 A set of possible strategies for each player strategy = complete action plan specifying what the player will do in every possible scenario that could arise in the game. Denote a generic strategy for player i by s i 3 A payoff/utility function u i for each player i Player i ’s utility could depend on the strategies chosen by all players, not just her own strategy. That is, u i is a function of the strategy profile : s = ( s 1 , s 2 , . . . , s n ) . Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 3 / 30
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Components of a Game Definition A Game consists of: 1 A set of players: 1 , . . . , n 2 A set of possible strategies for each player strategy = complete action plan specifying what the player will do in every possible scenario that could arise in the game. Denote a generic strategy for player i by s i 3 A payoff/utility function u i for each player i Player i ’s utility could depend on the strategies chosen by all players, not just her own strategy. That is, u i is a function of the strategy profile : s = ( s 1 , s 2 , . . . , s n ) . Note: This is sometimes also called a Normal-Form Game . Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 3 / 30
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Illustration Consider a game with two players, 1 and 2. Suppose player 1 has two strategies: a, b (so s 1 = a or s 1 = b ) Suppose player 2 has three strategies: c, d, e (so s 2 = c , s 2 = d , or s 2 = e ) Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 4 / 30
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Illustration Consider a game with two players, 1 and 2. Suppose player 1 has two strategies: a, b (so s 1 = a or s 1 = b ) Suppose player 2 has three strategies: c, d, e (so s 2 = c , s 2 = d , or s 2 = e ) Specifying the payoffs requires that we know the utilities of these two players for each of the eight possible strategy profiles: u 1 ( a, c ) u 2 ( a, c ) u 1 ( a, d ) u 2 ( a, d ) u 1 ( a, e ) u 2 ( a, e ) u 1 ( b, c ) u 2 ( b, c ) u 1 ( b, d ) u 2 ( b, d ) u 1 ( b, e ) u 2 ( b, e ) Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 4 / 30
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Depicting a 2-Player Game Using a Matrix Create a matrix (or table) with a row for each strategy for player 1 and a column for each strategy for player 2. Indicate the payoffs to each player for each strategy profile in the appropriate cell in the matrix. Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 5 / 30
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Depicting a 2-Player Game Using a Matrix Create a matrix (or table) with a row for each strategy for player 1 and a column for each strategy for player 2. Indicate the payoffs to each player for each strategy profile in the appropriate cell in the matrix.
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