Gorge offers Amanda to go hunting. If she refuses, they both get a payoff of 0. If she accepts (A), they go hunting. They are supposed to hunt boar but separate from one another once they arrive in the forest. Each of them must then decide (simultaneously) whether to hunt boar (B) as planned, or instead to go hunting rabbit (R). If both end up hunting rabbits, they each get a payoff of 1. If one of them hunts boar, while the other hunts rabbit, the one hunting rabbit gets a payoff of 1 and the other gets a payoff of −1. If they both hunt boar, then with probability 1/2, they both get a payoff of 5 and with probability 1/2, they both get a payoff of −1.

1. Describe this interaction as an extensive form game. 

2. Describe each player’s strategies.

3. Find the corresponding strategic form game.

4. Find all Nash equilibria in mixed strategies.

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