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Yale lectures 3 and 4 review

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

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  1. 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.

  2. Median Voter Theorem

  3. Median Voter Theorem

  4. Median Voter Theorem

  5. Median Voter Theorem

  6. Best ResponseNo dominated strategies

  7. 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.

  8. 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

  9. Mutual Best response graph if b=1/4

  10. Nash Equilibrium • If we are at a Nash Equilibrium, neither player has an incentive to deviate.

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