Country A is rich and country B is poor. Consequently, residents of country

B want to immigrate to country A. The trouble is that there is no legal way

to do. So they attempt to cross the border illegally. There are 3 border crossings

at which a resident of B may attempt to cross the border. An attempt

is successful if there is no border guard at the crossing, and unsuccessful if

there is a guard at the crossing. Country A has only 1 border guard. Model

the game in which a resident of country B attempts to enter country A at

one of the 3 border crossings, and the government of country A chooses to

post its border guard at one of the 3 border crossings. In this game, each

player has three pure strategies.

(a) What are the ultimate outcomes in this game?

(b) What are the player's Bernoulli payoffs?

(c) Find a mixed strategy equilibrium of the game. [((1/3, 1/3, 1/3), (1/3,

1/3, 1/3))]