##### Two players are contesting a resource worth v > 0. Each can be a dove (passive) or a hawk (aggressive). If one is aggressive and the other passive, the aggressive opponent gets the resource. If both are passive, each obtains the resource with equal likelihood. If both are aggressive, both players incur cost c, and each obtains the resource with equal 1 likelihood. We assume c is large relative to the value of the good, c > v/2. Write down the set of strategies. Then, in the form of a payoff matrix, write the payoffs each player gets from each strategy profile. Finally, find all pure Nash equilibria.

Two players are contesting a resource worth v > 0. Each can be a dove (passive) or a

hawk (aggressive). If one is aggressive and the other passive, the aggressive opponent

gets the resource. If both are passive, each obtains the resource with equal likelihood. If

both are aggressive, both players incur cost c, and each obtains the resource with equal

1

likelihood. We assume c is large relative to the value of the good, c > v/2. Write down

the set of strategies. Then, in the form of a payoff matrix, write the payoffs each player

gets from each strategy profile. Finally, find all pure Nash equilibria.