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Behavioural Economics ECON3124
Problem Set 4
The players know each others’ utilities.
Show that a Nash equilibrium of this game is for the investor to send all $10 and the entrepreneur to
split the $30 equally.
(c) [5pts] Going back to looking only at the payoffs. Argue informally but carefully that the
above is NOT a fairness equilibrium in Rabin's intentions-based model of social preferences.
(d) Researchers find that entrepreneurs are often more generous in the Trust Game (if
investors send all $10) than in a dictator game in which they are asked to split $30. Show
whether this finding can be explained by (i) [3pts] a distributional model of social
preferences; and (ii) [10pts] Rabin's model of intentions-based preferences.
2. A large population of players are playing the following version of the beauty-contest
game. Each player guesses a number between 100 and 200 (inclusive), and the player
closest to p < 1 of the average wins a given prize. If multiple players are closest to p < 1
times the average, the prize is allocated randomly between them.
(a) [5pts] What guess(es) survive iterated elimination of dominat ed strategies?
From now on, suppose that a fraction 1 − of the players is rational, and a fraction of the
players is irrational. It is known that irrational players like high numbers, so they always
guess 200.
(b) [10pts] Solve for the rationals' equilibrium guess as a function of and .
(c) [5pts] What happens to the rationals' guess as approaches 1 from below? Explain the
intuition.
(d) [5pts] What happens to the rationals' guess as approaches 1? Explain the intuition.