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Unformatted text preview: Game Theory: Dominant and Dominated Strategies Todd Sarver Northwestern University Econ 3102 Fall 2011 Todd Sarver (Northwestern University) Game Theory Econ 3102 Fall 2011 1 / 30 Outline 1 Components of a Game 2 Examples 3 Solution Concepts Dominant Strategies Iterated Elimination of Strictly Dominated Strategies 4 NonDominance Solvable Games 5 Pareto Efficiency Todd Sarver (Northwestern University) Game Theory Econ 3102 Fall 2011 2 / 30 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 3102 Fall 2011 3 / 30 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 NormalForm Game . Todd Sarver (Northwestern University) Game Theory Econ 3102 Fall 2011 3 / 30 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 3102 Fall 2011 4 / 30 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 3102 Fall 2011 4 / 30 Depicting a 2Player 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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This note was uploaded on 01/03/2012 for the course ECON 3102 taught by Professor Sarver during the Spring '08 term at Northwestern.
 Spring '08
 SARVER
 Microeconomics, Game Theory

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