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

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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) ? ?A max(xA ?xB, 0),

UB = xB ? ?B max(xA? xB, 0).

(a) Suppose that the two agents play a dictator game in whichplayer 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'sstrategy for all possible values of ?A.

(b) Now suppose that the two agents are playing an ultimatumgame with an endowment of 100. Write down the set of players, thepure 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 dependon ?B and ?A?

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