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In: Advanced Math

3. Dictator and Ultimatum Games with Fehr-Schmidt Preferences. Now let the two utility functions be given...

3. Dictator and Ultimatum Games with Fehr-Schmidt Preferences. Now let the two utility functions be given by,

UA = xA − .6 max(xB − xA, 0) − βA max(xA − xB, 0),

UB = xB − αB max(xA − xB, 0).

(a) Suppose that the two agents play a dictator game in which player A is given an endowment of 100 and may transfer any amount s ∈ [0, 100] to player B. The material payoffs are then given by (xA, xB) = (100 − s, s). Compute player A's strategy for all possible values of βA.

(b) Now suppose that the two agents are playing an ultimatum game with an endowment of 100. Write down the set of players, the pure strategy space of each player and the payoff functions.

(c) Calculate B's best response to every offer s ∈ [0, 100].

(d) How does the subgame perfect equilibrium of the game depend on αB and βA?

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Colby Messinger answered 7 months ago
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