Country A is rich and country B is poor. Consequently, residents of countryB 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 cross- ings 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.
Can you please show the solution algebraically and on a graph? Thank you!