9. Solutions to the Exercises

This chapter contains hints to the solutions of the exercises. The topics include stable matchings, Vickrey auctions, Blackwell approachability, Farkas’ lemma, duality in linear programming, duels, Cournot competition, supermodular games and Tarski’s fixed point theorem, convex games, potential games, dissipative games, fictitious play and the Shapley triangle, the game of Chomp, a poker game, bargaining, a double auction, the possibly negative value of information, strategic transmission of information, correlated equilibrium distribution via minmax, comparison between correlated and Nash equilibria, the prisoner’s dilemma with a blind player, the battle of the sexes in the dark, jointly rational payoffs, subgame-perfect equilibrium payoffs for discounted games and quitting games.