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 payoff of 1 and the other country gets a payoff of -1 . If the countries split which locations they win, then the war is a stalemate and they each get a payoff of O.