Since the seminal paper of Nash (1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. We study the properties of these strategies in 2-player non-zero-sum strategic games, whose Nash equilibria are only mixed.

This paper characterizes the set of equilibrium networks in the two-way flow model of network formation with small decay, and this for all increasing benefit functions of the players. We show that as long as the population is large enough, this set contains large- as well as small-diameter...