?? E XERCISE 181.1 (Variants of ultimatum game and impunity game with equity- conscious players)…
?? EXERCISE 181.1 (Variants of ultimatum game and impunity game with equity- conscious players) Consider variants of the ultimatum game and impunity game in which each person cares not only about the amount of money she receives, but also about the equity of the allocation. Specifically, suppose that person i’s prefer-
ences are represented by the payoff function given by ui (x1, x2)= xi- ßi|x1 – x2|,
where xi is the amount of money person i receives, ßi > 0, and, for any number
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z, |z| denotes the absolute value of z (i.e. |z| = z if z > 0 and |z| = -z if z 0).
Find the set of subgame perfect equilibria of each game and compare them. Are there any values of ß1 and ß2 for which an offer is rejected in equilibrium? (An interesting further variant of the ultimatum game in which person 1 is uncertain about the value of ß2 is considered in Exercise 222.2.)