04 Jun Question ECN 122 Game Theory: Homework 1
Question
ECN 122 Game Theory: Homework 1
Deadline for graded problems: Friday, April 10, 2015, 10:00 am in class
Practice Problems
Exercise 5.3 (Altruistic preference)1 Person 1 cares about both her income and person 2’s income. Precisely, the value she attaches to each unit of her own income is the same as the value she attaches to any two units of person 2’s income. For example, she is indi erent between a situation in which her income is 1 and person 2’s is 0, and one in which her income is 0 and person 2’s is 2. How do her preferences order the outcomes (1; 4), (2; 1), and (3; 0), where the rst component in each case is her income and the second component is person 2’s income? Give a payo function consistent with these preferences.
Exercise 17.1 (Games equivalent to the Prisoners’ Dilemma) Determine whether each of the games in Figure 17.1 di ers from the Prisoners’ Dilemma only in the names of the players’ actions, or whether it di ers also in one or both of the players’ preferences.
X
Y
X
Y
X
3,
3
1,
5
X
2, 1
0, 5
Y
5,
1
0,
0
Y
3, -2
1, -1
Figure 17.1 The strategic games for Exercise 17.1.
Graded Problems
Exercise 18.1 (Hermaphroditic sh) Members of some species of hermaphroditic sh2 choose, in each mating encounter, whether to play the role of a male or a female. Each sh has a preferred role, which uses up fewer resources and hence allows more future mating. A sh obtains a payo of H if it mates in its preferred role and L if it mates in the other role, where H > L. (Payo s are measured in terms of number of o spring, which sh are evolved to maximize.) Consider an encounter between two sh whose
1Exercise numbers match the ones in the book.
2Think of Nemo.
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