The Computational Complexity of Equilibria with Strategic Constraints

Abstract: Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to address issues of tractability, attention has been given to approximate versions of these problems. Our work extends this direction by considering games with constraints in which players are subject to some form of restrictions on their strategic choices. We also consider the relationship between Nash equilibria and so-called constrained or social equilibria in this context, with particular attention to how they are related with respect to totality and complexity. Our results demonstrate that the computational complexity of finding an equilibrium varies significantly between games with slightly different strategic constraints. In addition to examining the computational aspects of such strategic constraints, we also demonstrate that these constraints are useful for modeling problems involving strategic resource allocation and also are of interest from the perspective of behavioral game theory.