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Lecture 4: Quick Recap of Our Concepts () Game Theory: Recap of Lectures 1-3 January 30, 2017 1 / 8
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Pure Strategy Nash Equilibrium De°nition In 2-player games, a (pure strategy) NE is an action pair ( s 1 , s 2 ) such that s 1 is a best response for P1 to s 2 , and s 2 is a best response for P2 to s 1 . De°nition In N-player games, a (pure strategy) NE is an action vector ( s 1 , s 2 , ..., s N ) such that for every player i , s i is a best response to s ° i . idea: at equilibrium, each player correctly anticipates what his opponents will do, and best-responds to it, i.e. chooses an action that maximizes his own payo/ taking as given what he expects the opponents to do () Game Theory: Recap of Lectures 1-3 January 30, 2017 2 / 8
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NE Tips if I ask you to show that a given vector of actions ( s 1 , ..., s N ) is a NE, you need to check that each player is best-responding to the others: assuming that everyone else sticks with the plan, i.e. plays their part of ( s 1 ..., s N ) , is your action s i optimal for you? if every player can answer ±yes², then it is a NE if I ask you to show that a given vector ( s 1 , ..., s N ) is not a NE, you need to °nd someone (just one is enough) who can pro°tably deviate: °nd a player who should realize that if everyone else sticks with the
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