On a Network Generalization of the Minmax Theorem

We consider graphical games in which edges are zero-sum games between the endpoints/players; the payoff of a player is the sum of the payoffs from each incident edge. We give a simple reduction of such games to two-person zero-sum games; as a corollary, a mixed Nash equilibrium can be computed efficiently by solving a linear program and rounding off the results. The same is true when the games on the edges belong to the more general class of strictly competitive games. Such games are arguably very broad and useful models of networked economic interactions. Our results extend, make polynomially efficient, and simplify considerably the approach in [2]. ∗Microsoft Research, New England. †UC Berkeley.