A planning committee with three members, A, B, and C, is trying to decide whether or not to propose two new projects for the city, a library and a movie theater. Each member feels that the required increase in taxes would create a disutility of 10; the theater would generate a benefit of 40 for A, while the library would generate a benefit of 40 for B; C is not interested in either
option. A majority vote will determine which, if any, projects should be proposed. Since C does not value the library or the theater, it would never be a rationalizable strategy for him to vote for either project. Thus, the support of both A and B is required for a proposal to pass under majority voting.
(a) From the set {Library Only, Theater Only, Library and Theater, Neither}, which voting strate-gies are rationalizable for A and B? What are the corresponding payoffs?
(b) If A and B could cooperate on their voting decision, what would they do?
(c) If binding agreements between A and B were not possible, explain why your answer in
(d) cannot be a Nash equilibrium.