# game theory

**alienware**

There are d democrats and r republicans voting in the US Presidential election. Each person decides whether to vote or not vote. The voters get a payoff of 2,1,0 if their preferred candidate wins, ties, or loses (respectively). Voters that vote incur a cost of 0<c<1(which leads to respective payoffs of 2-c, 1-c, -c, c).

a) Suppose that d = r = 1. Write out the normal form game table, tell what game this is,and determine the Nash equilibrium.b) Now Suppose d = r > 1, find the set of Nash equilibrium. Hints: Is there any NE in which everyone votes? Is there any NE in which there is a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?c) Now Suppose d a) Suppose that d = r = 1. Write out the normal form game table, tell what game this is,and determine the Nash equilibrium.b) Now Suppose d = r > 1, find the set of Nash equilibria. Hints: Is there any NE in whicheveryone votes? Is there any NE in which there is a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?c) Now Suppose d a) Suppose that d = r = 1. Write out the normal form game table, tell what game this is,and determine the Nash equilibrium.b) Now Suppose d = r > 1, find the set of Nash equilibrium. Hints: Is there any NE in which everyone votes? Is there any NE in which there is a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?c) Now Suppose d <r, find the set of Nash equilibrium.

- 8 years ago
- 5

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