Four political candidates are deciding whether or not to enter a race for an ele

Question

Four political candidates are deciding whether or not to enter a race for an elected office where the decision depends on who else is throwing his or her hat into the ring. Suppose candidate A prefers not to enter if candidate B is expected to enter; otherwise, A prefers to enter. Candidate B prefers not to enter if she expects either candidate A and/or candidate D to enter; other-wise, she prefers to enter. Candidate C prefers not to enter if he expects candidate A to enter and prefers to enter in all other cases. Candidate D prefers not to enter if either candidate B and/or C are expected to enter; otherwise, she prefers to enter. If we assume that their choices are consistent with Nash equilibrium, who will enter the race?

Explanation / Answer

Nash equilibrium will be either B and C enters the race or A and D enters the race.

These are the only possible solutions that can be there.

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