Probability

You are given the following game, representing the battle of Stalingrad. The payoffs

measure expected casualties on the opponent’s side, counted in 100,000s. Assume risk

neutrality on both sides (i.e. ui(x)=x).

Soviet Union

Hold

Ground

Flee

Germany Full 2 1 2 3

force

Keep 1 3 3 2

reserves

a. Find all the game’s Nash equilibria.

b. The game represents a war with payoffs counted in hundreds of thousands of

casualties. We can assume that each side’s casualties are viewed negatively by itself

and positively by the rival. Is the game a mixed-motive game? If so, how is this

possible, given the previous statement? Explain. Refer to the payoff matrix in your

answer.

c. Do the players have an interest in coordinating their strategies in this game?

Explain.

d. Find all the game’s Nash equilibria if players have the following risk function:

e. Are players in section d risk-loving or risk-neutral?