Consider the following game. Players 1 and 2 are partners in a firm. If they both invest 10 in a project, the project will achieve an income of 13 per person, so both will get net earnings of 3. If only one of them invests, the project earns only 5 per person, leading to a payoff of -5 for the person who invested and 5 for the other. If none of them invests, both get nothing. They can only choose to invest 10 or not invest at all. 1. Write down the payoff matrix of the game. 2. Assume that both players only care about their own material payoffs. Suppose these preferences are commonly known to both players. Derive the Nash equilibrium/equilibria of the game. Does a player’s best
Consider the following game. Players 1 and 2 are partners in a firm. If they both invest 10 in
a project, the project will achieve an income of 13 per person, so both will get net earnings
of 3. If only one of them invests, the project earns only 5 per person, leading to a payoff of
-5 for the person who invested and 5 for the other. If none of them invests, both get nothing.
They can only choose to invest 10 or not invest at all.
1. Write down the payoff matrix of the game.
2. Assume that both players only care about their own material payoffs. Suppose these
preferences are commonly known to both players. Derive the Nash equilibrium/equilibria
of the game. Does a player’s best choice depend on the strategy chosen by the other
player?
Step by step
Solved in 2 steps with 2 images
