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Respond to the question: Game Theory of Elections?

01/17/2010 10:51 AM by Michael; Game Theory of Elections
Two candidates, A and B, compete in an election. Of the n citizens, k support candidate A and m(=n-k) support candidate B. Each citizen decides whether to vote, at a cost, for the candidate she supports, or to abstain. A citizen who abstains receives the payoff of 2 if the candidate she supports wins, 1 if this candidate ties for first place, and 0 if this candidate loses. A citizen who votes receives the payoffs 2-c, 1-c, and c in these three cases, where 0<c<1.
a) For k=m, find the set of NE. (Is the action profile in which everyone votes a NE? Is there any NE in which the candidates 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 two or more votes?)
b) What is the set of NE for k<m? [Manage messages]