(with Rajiv Vohra), August 2018.
Dedicated to Tapan Mitra — advisor, colleague and dear friend. Tapanda, your sense of aesthetics, minimalism and rigor has been an inspiration to us. We hope you will find some reflection of it in these pages.
Summary. A game of love and hate is one in which a player’s payoff is a function of her own action and the payoffs of other players. For each action profile, the associated payoff profile solves an interdependent utility system, and if that solution is bounded and unique for every profile we call the game coherent. Coherent games generate a standard normal form. Our central theorem states that every Nash equilibrium of such a game is Pareto optimal.