We mentioned in this chapter that the incentives of the prisoners’ dilemma appear frequently in real world situations.

A: In each of the following, explain how these are prisoners’ dilemmas and suggest a potential solution that might address the incentive problems identified in such games.

(a)When I teach the topic of prisoners’ dilemmas in large classes that also meet in smaller sections once a week, I sometimes offer the following extra credit exercise: Every student is given 10 points. Each student then has to decide how many of these points to donate to a “section account” and convey this to me privately. Each student’s payoff is a number of extra credit points equal to the number of points they did not donate to their section plus twice the average contribution to the section account by students registered in their section. For instance, if a student donates 4 points to his section and the average student in the section donated 3 points, then this student’s payoff would be 12 extra credit points—6 because the student only donated 4 of his 10 points, and 6 because he gets twice the average donated in his section.

(b) People get in their cars without thinking about the impact they have on other drivers by getting on the road — and at certain predictable times, this results in congestion problems on roads.

(c) Everyone in your neighborhood would love to see some really great neighborhood fireworks on the next national independence day — but somehow no fireworks ever happen in your neighborhood.

(d) People like downloading pirated music for free but would like to have artists continue to produce lots of great music.

(e) Small business owners would like to keep their businesses open during “business hours” and not on evenings and weekends. In some countries, they have successfully lobbied the government to force them to close in the evenings and weekends. (Laws that restrict business activities on Sunday are sometimes called blue laws.)

B: In Chapter 21, we introduced the Coase Theorem, and we mentioned in Section 21A.4.4 the example of bee keeping on apple orchards. Apple trees, it turns out, don’t produce much honey (when frequented by bees), but bees are essential for cross-pollination.

(a) In an area with lots apple orchards, each owner of an orchard has to insure that there are sufficient numbers of bees to visit the trees and do the necessary cross-pollination. But bees cannot easily be kept to just one orchard—which implies that an orchard owner who maintains a bee hive is also providing some cross-pollination services to neighboring orchards. In what sense to orchard owners face a prisoners’ dilemma?

(b) How does the Coase Theorem suggest that orchard owners will deal with this problem?

(c) We mentioned in Chapter 21 that some have documented a “custom of the orchards” — n implicit understanding among orchard owners that each will employ the same number of bee hives per acre as the other owners in the area. How might such a custom be an equilibrium outcome in a repeated game with indefinite end?