06-01-Game-Theory-I.pdf - Game Theory I CSE 440 Today I...

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Game Theory I CSE 440
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Today I Game Theory
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From Games to Game Theory I Game theory is the study of strategic decision making (of more than one player) I Used in economics, political science etc. John Nash Heinrich Freiherr von Stackelberg John von Neumann Winners of Nobel Memorial Prize in Economic Sciences
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Normal-Form Games I A game in normal form consists of
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N }
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N } I Set of strategies S = Q n i =1 S i
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N } I Set of strategies S = Q n i =1 S i I Payoffs / Utility functions u i : S R I u i ( S 1 , . . . , S n )
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N } I Set of strategies S = Q n i =1 S i I Payoffs / Utility functions u i : S R I u i ( S 1 , . . . , S n ) I Players move simultaneously and the game ends immediately afterwards.
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N } I Set of strategies S = Q n i =1 S i I Payoffs / Utility functions u i : S R I u i ( S 1 , . . . , S n ) I Players move simultaneously and the game ends immediately afterwards. I Strategy profile s = < s 1 , . . . , s n >, s i S i
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N } I Set of strategies S = Q n i =1 S i I Payoffs / Utility functions u i : S R I u i ( S 1 , . . . , S n ) I Players move simultaneously and the game ends immediately afterwards. I Strategy profile s = < s 1 , . . . , s n >, s i S i I Outcome / Utility profile u ( s ) = < u 1 ( s ) , . . . , u n ( s ) >
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N } I Set of strategies S = Q n i =1 S i I Payoffs / Utility functions u i : S R I u i ( S 1 , . . . , S n ) I Players move simultaneously and the game ends immediately afterwards. I Strategy profile s = < s 1 , . . . , s n >, s i S i I Outcome / Utility profile u ( s ) = < u 1 ( s ) , . . . , u n ( s ) > I Zero-Sum Game: i u i ( s ) = 0 s
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Normal-Form Games I A game in normal form consists of I Set of players N = { 1 , . . . , N } I Set of strategies S = Q n i =1 S i I Payoffs / Utility functions u i : S R I u i ( S 1 , . . . , S n ) I Players move simultaneously and the game ends immediately afterwards. I Strategy profile s = < s 1 , . . . , s n >, s i S i I Outcome / Utility profile u ( s ) = < u 1 ( s ) , . . . , u n ( s ) > I Zero-Sum Game: i u i ( s ) = 0 s I Also called: Matrix-Form or Standard-Form
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Normal-Form Games: Example 1 I Prisoner’s Dilemma I Two suspects are charged with a crime I If both Co-operate: 1 year in jail each I If one Defect (rat out the other person), one Cooperate: 0 year for (D), 3 years for (C) I If both Defect: 2 years in jail each
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Normal-Form Games: Example 1 I Prisoner’s Dilemma I Two suspects are charged with a crime I If both Co-operate: 1 year in jail each I If one Defect (rat out the other person), one Cooperate: 0 year for (D), 3 years for (C) I If both Defect: 2 years in jail each I Variation: split or steal
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Normal-Form Games: Example 2 I Rock Paper Scissors I Rock beats Scissors I Scissors beats Paper I Paper beats Rock
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