A king is deciding where to hide his treasure, while a pirate is deciding where to look for the treasure. The payoff to the king from successfully hiding the treasure is 5 and from having it found is 2. The payoff to the pirate from finding the treasure is 9 and from not finding it is 4. The king can hide it in location X or Z. Each player maximizes its payoff

Suppose the pirate has two pure strategies: inspect X or inspect Z.

Find a mixed strategy Nash equilibrium where pp is the probability the treasure is hidden in X and 1p1p that it is hidden in Z and q is the probability that the pirate inspects X:

Select an answer:

a. p = 5/9q-3/5 b. p = 2/5q = 4/9 c. p = 4/9q =2/5 d. p = q = 1/2 e. I don't know