The notion of S-modularity was developed by Glasserman and Yao in the context of optimal control of queueing networks. S-modularity allows the objective function to be supermodular in some variables and submodular in others. It models both compatible and conflicting incentives, and hence conveniently accommodates a wide variety of applications. This paper introduces S-modularity into the context of n-player noncooperative games. This generalizes the well-known supermodular games of Topkis, where each player maximizes a supermodular payoff function (or equivalently, minimizes a submodular payoff function). The paper illustrates the theory through a variety of applications in queueing systems.
