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2 candidates A,B compete in an election. Of the n...

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2 candidates A,B compete in an election. Of the n citizens, k support candidate A and the remaining (n - k) support B. Each citizen whether to abstain, or to vote at a cost. A citizen who abstains receives payoff 2 if the candidate she supports wins, 1 if this candidate ties for 1st place, and 0 if the candidate loses. A citizen who votes receives the same payoffs, minus a voting cost 0 < c < 1: Assume that k ?n/2. Find p such that the following is a NE:  -each candidate who supports A votes w.p. p  -k of the B-supporters each vote w.p. 1  -the remaining n - 2k B-supporters all abstain. How does voter turnout depend on c? Also, note: if every A supporter votes w.p. p; then the probability that all k of them vote is p^k; and the probability that exactly (k-1) of them vote is (kp^(k-1))(1 - p).

 

Paper#13406 | Written in 18-Jul-2015

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