高级微观-博弈论
4页1、高级微观-博弈论Econ711February32014Peter NormanAssignment41. Consider a prisoners dilemma with stage game payors c dC2;20;3D3;01;1played twice.1.Sketch the extensive form.2. How many nodes are there in the extensive form?How many information sets?How many purestrategies?3. Write down the payomatrix for the reduced normal form.Assume that there is no discounting.4. Find all pure strategy Nash equilibria of the reduced normal form game.5. What are all Nash equilibria for the regular normal form?For each
2、equilibrium,specify the equilibrium outcome and determine which equilibria are subgame perfect.6. Which strategies survive iterated elimination of strictly dominated strategies?Which strategiessurvive iterated elimination of weakly dominated strategies?7. Now consider an arbitrary.nite horizon T:Prove that no player can play C on the equilibrium path.8. Given an arbitrary.nite horizon T,write down a strategy pro.le that is a Nash equilibrium,but notsubgame perfect.2. Consider the normal form gam
3、ec d A d BC3;3 2;4 2;4D A4; 22;2 1; 1D B4; 2 1; 10;0l. Find all Nash equilibria(pure and mixed).2.Suppose that the stage game is played twice and that payors are not discounted.Construct a subgameperfect equilibrium in which(C;c)is played in the.rst period?3.Suppose that the stage game is repeated4times.Construct a subgame perfect equilibrium where(D A;c)is played in the.rst period?4.Consider the following outcome path(D A;d B);(D B;d A);(D A;d A);(D A;d A);:;(D A;d A):Con-struct a strategy pro.
4、le that supports this as a subgame perfect equilibrium in the T repeated game.What is the smallest value of T for this to work3. Consider an in.nite repetition of c dC2;20;3D3;01;1and assume payors are discounted by 2(0;1):1. For large enough,construct a subgame perfect equilibrium where(C;c)is played in every periodontheequilibriumhttp:/ Nash reversion in your construction and.nd a critical value for .2. Change the stage game top c dP 1; 1 1; 1 1;0C 1; 12;20;3D0; 13;01;1Assuming strategies rely
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