  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.
