GT4-mixed - Overview So far Mixed Strategies UGBA 143 Game...

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1 1 Mixed Strategies UGBA 143: Game Theory and Business Decisions 2 Overview So far: Used Nash equilibrium to solve games Strategic outcome in which no player would unilaterally deviate to choose another strategy Next: What happens when we cannot find a Nash equilibrium using earlier methods? Randomized strategies 3 A Simple Game Alice and Bob simultaneously show palms-up or palms-down Alice wins if they match and Bob wins otherwise (stake is \$10) Each should randomize 50-50 between the two choices Up Down Down Up 10 -10 -10 10 10 -10 10 -10 Alice Bob 4 Pure versus mixed strategies Pure strategy: choose one strategy for sure Mixed strategy: randomize among several options There is no pure-strategy Nash equilibrium None of the four pure-strategy action profiles (U,U), (U,D), (D,U), (D,D) is a NE Randomizing 50-50 by both players is called a mixed-strategy Nash equilibrium When both randomize 50-50, neither can do any better by switching his/her own randomization probabilities 5 Mixed strategies What if the stakes change?

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