Please see question below:

There are two players, A and B. Each player i E {A, B} can be of one of two types ti E {1, 2}. The probability that a player is of type 2 equals 7. When A and B meet, each can decide to fight or cave. If both players fight, then player i gets payoff ti titt; - c, j # i where c > 0. If player i fights, but player j does not, then player i gets payoff 1, while player j gets payoff 0. If both players do not fight, each gets payoff 1/2