Suppose Dean and Kennedy are playing a single stage game. Each simultaneously chooses either 1 or 2. If they both select 1, Dean pays Kennedy $2. If they both pick 2, Dean pays Kennedy $4. If they select different numbers, Kennedy pays Dean $3. Draw a table showing the two players' strategies and payoffs. Are any strategies dominant? Weakly dominant? Dominated? Solve for a mixed strategy equilibrium.

Question

The payoff matrix should appear as follows:





What will be an ideal response?

Answer 1

There are no dominant, weakly dominant or dominated strategies. A mixed strategy is found the following way: If P represents the probability Kennedy chooses 1, Dean's expected payoff for selecting 1 is and his expected payoff for selecting 2 is . Kennedy's choice of P that makes Dean indifferent between 1 and 2, so that he randomizes between them is . Similarly, if Q represents the probability that Dean chooses 1, Kennedy's expected payoff from choosing 1 is and her expected payoff from choosing 2 is . Dean's choice of Q that makes Kennedy indifferent between 1 and 2, so that she randomizes between them is . Thus a mixed strategy equilibrium is that both Dean and Kennedy choose 1 with a probability of 7/12 and 2 with a probability of 5/12.