5. There are two countries that are battling in two locations: location A and location B. Suppose…

5. There are two countries that are battling in two locations: location A and

location B. Suppose that each country has 2 divisions in its army. Divisions cannot

be subdivided, so a country must choose either to put both divisions at Location

A, both at Location B, or to put one division at location A and one at location B.

If a country has more divisions at one location, then they win that location. If the

countries have the same number of divisions at a location, then each country wins

that location with a probability of 1/2. A country wins if it wins both locations

and then it gets a payo of 1 and the other country gets a payo of -1. If the

countries split which locations they win, then the war is a stalemate and they each

get a payo of 0.

(a) Find all the pure and mixed strategy equilibria of this game (hint: writing

out the payo matrix for the normal form will make this fairly easy).

(b) Now suppose that both countries have three divisions (so they can put three

divisions at one location or two at one location and one at the other location). Find

all the pure and mixed equilibria of the game.

(c) Consider a variation of the game where one country has three divisions

and the other has only two divisions. Draw the normal form payo matrix for the

game and enter the expected payos.

(d) Find all of the pure strategy equilibria for the game in (c).