Congestion, Coordination and Matching

We study the existence of pure strategy Nash equilibria in finite congestion and coordination games. Player set is divided into two disjoint groups, called men and women. A man choosing an action a is better off if the number of other men choosing a decreases, or if the number of women choosing a increases. Analogously, a woman becomes better off if more men or fewer women choose the same action as she does. Existence proofs are constructive: we build simple "best reply" algorithms that converge to an equilibrium.