1. There are two hunters (Hunter 1 and Hunter 2) who can hunt for either a wild horse or a rabbit that they can sell in the market. Hunting wild horses is challenging and requires mutual cooperation. If either one of them hunts a wild horse alone, then the wild horse will surely get away. A Wild horse has a market price of 1,000 AUD. On the other hand, hunting a rabbit is an individualistic endeavour that is not done in pairs, and whoever chooses to hunt a rabbit can surely catch one. A rabbit has a market price of 50 AUD. The payoffs for this game are as follows: (12 Marks)

Wild Horse Wild Horse 500 , 500

Rabbit 50 , 0

Rabbit 0 , 50 50 , 50

a) Identify the dominant strategy of each player. (2 Marks)

b) Find the pure-strategy Nash equilibrium or equilibria. (2 Marks)

c) Compute the mixed-strategy Nash equilibrium. As part of your answer, draw the best-

response function diagram for the mixed strategies. (2 Marks)

d) Suppose the game is played sequentially, with Hunter 1 moving. What is/are hunter 2's

contingent strategie/s? Write down the normal and extensive forms for the sequential

version of the game. (2 Marks)

e) Using the normal form for the sequential version of the game, solve for the Nash

equilibria. (2 Marks)

f) Identify the proper sub-games in the extensive form for the sequential version of the

game. Use backward induction to solve for the sub-game perfect equilibrium. Explain why the other Nash equilibria of the sequential game are "unreasonable." (2 Marks)

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