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.

翻译：解概念（如纳什均衡）的计算方面已被广泛研究，包括最终目标是寻找具有某些额外性质的均衡的场景。此外，为解决可处理性问题，注意力已转向这些问题的近似版本。我们的工作通过考虑具有约束的博弈（其中玩家的战略选择受到某种形式的限制）来扩展这一方向。我们还研究了纳什均衡与所谓约束均衡或社会均衡在此背景下的关系，特别关注它们在整体性和复杂性方面的关联。我们的结果表明，在具有略微不同战略约束的博弈之间，寻找均衡的计算复杂性存在显著差异。除了考察这种战略约束的计算方面外，我们还证明这些约束对于建模涉及战略资源分配的问题很有用，并且从行为博弈论的角度来看也具有研究价值。