Proble: Game theory- solve

Posted by Atika Gupta on Mar 11, 2014; 12:53pm
URL: http://discussion-forum.276.s1.nabble.com/Proble-Game-theory-solve-tp7585164.html

Ques: Suppose that 100 people live in a village where an election is being held. 51 villagers support the conservative candidate (A) and 49 support the liberal candidate (B). The candidate getting the most vote wins. In case of a tie the winner is decided by the toss of a fair coin. A villager gets a payoff of +10 units of utility if her favourite candidate gets elected and a payoff of -10 units of utility if the opposition gets elected. But voting is a nuisance that costs voters one unit of utility. Those who stay at home and do not vote evade this cost, but are rewarded or punished just the same as those who shoulder the cost of voting.
Which of the following statements is correct?

a. In the above game nobody choosing to vote is a nash equilibrium outcome.
b. There is no nash equilibrium outcome in which everybody chooses to vote.
c. One pure strategy nash equilibrium outcome is:
    All the supporters of the conservative candidate vote for A and all the supporters of the liberal candidate vote for B.
d. none of the above.