Yale lectures 3 and 4 review Iterative deletion of dominated strategies. Ex: two players choose positions on political spectrum. Endpoints become repeatedly.

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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 ,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5, ,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5, ,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5, ,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5, ,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

Median Voter Theorem ,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5, ,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5, ,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5, ,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5, ,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

Median Voter Theorem ,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5, ,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5, ,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5, ,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5, ,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

Median Voter Theorem ,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5, ,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5, ,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5, ,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5, ,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

Best Response No dominated strategies leftright U5,10,2 M1,34,1 R4,22,3

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. s 1 and s 2 are effort levels. Max s1 2(s 1 + s 2 +bs 1 s 2 ) –(s 1 ) 2 Use calculus – differentiate and set to zero 2(1+bs 2 ) –2(s 1 ) = 0 1+bs 2 =(s 1 ) Best response function for s 1 1+bs 1 =(s 2 ) Best response function for s 2 if equal (as symmetric), 1+b(1+bs 1 ) =(s 1 ) s 1 = 1/(1-b) Your share of the profit Your cost of effort

Mutual Best response graph if b=1/4

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