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Yale lectures 3 and 4 review. Iterative deletion of dominated strategies. Ex: two players choose positions on political spectrum. Endpoints become repeatedly eliminated by deletion of dominated strategies. Median Voter Theorem. Median Voter Theorem. Median Voter Theorem.
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Yale lectures 3 and 4 review • Iterative deletion of dominated strategies. • Ex: two players choose positions on political spectrum. Endpoints become repeatedly eliminated by deletion of dominated strategies.
In this case… • Each of player 1’s actions is a best response to some mixed strategy of player 2. • If you have an action that is never a best response, don’t play it. • The best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given.
Finding a mutual best response Partnership game b is synergy. s1 and s2 are effort levels. Max s1 2(s1 + s2 +bs1s2) –(s1)2 Use calculus – differentiate and set to zero 2(1+bs2) –2(s1) = 0 1+bs2 =(s1) Best response function for s1 1+bs1 =(s2) Best response function for s2 if equal (as symmetric), 1+b(1+bs1) =(s1) s1 = 1/(1-b) Your share of the profit Your cost of effort
Nash Equilibrium • If we are at a Nash Equilibrium, neither player has an incentive to deviate.