Consider the following “Battle of the Sexes” game. Bob prefers to attend a hocke

Question

Consider the following “Battle of the Sexes” game. Bob prefers to attend a hockey game but only if Jan will accompany him; Jan feels the same way about a concert on the same night. Their payoffs from the possible outcomes are shown below.

Is there a pure strategy Nash Equilibrium to this game? What is it?

What probabilities do Bob and Jan choose in the mixed strategy equilibrium?

Are Bob and Jan better off with mixed strategies compared to any pure strategy?

Explanation / Answer

There will be two nash equilibrium (Hockey,Hockey) and (Concert,Concert).

Let Jan will choose hockey with probability p. He will choose hockey iff:

2p > 4(1-p) => p>2/3

Let Bob choose hockey with probability q. He will choose hockey iff:

4q > 2(1-q) => q>1/3

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