Counterfactual policy evaluation often requires computation of game‐theoretic equilibria. We provide new algorithms for computing pure‐strategy Nash equilibria of games on networks with finite action spaces. The algorithms exploit the fact that many agents may be endowed with types such that a particular action is a dominant strategy. These agents can be used to partition the network into smaller subgames whose equilibrium sets may be more feasible to compute. We provide bounds on the complexity of our algorithms for models obeying certain restrictions on the strength of strategic interactions. These restrictions are analogous to the assumption in the widely used linear‐in‐means model of social interactions that the magnitude of the endogenous peer effect is bounded below one. For these models, our algorithms have complexity O_p(n^c), where the randomness is with respect to the data‐generating process, n is the number of agents, and c depends on the strength of strategic interactions. We also provide algorithms for computing pairwise stable and directed Nash stable networks in network formation games.

中文翻译：

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离散网络游戏中的平衡计算

反事实政策评估通常需要计算博弈论平衡。我们提供了用于在具有有限动作空间的网络上计算游戏的纯策略Nash均衡的新算法。该算法利用了这样一个事实，即许多代理可以被赋予类型，以使特定的动作成为主导策略。这些代理可以用来将网络划分为较小的子博弈，其平衡集可能更易于计算。我们为模型提供了算法复杂性的界限，服从了对战略互动强度的某些限制。这些限制类似于广泛使用的社会互动的均值线性模型中的假设，即内生同伴效应的幅度被限制在一个以下。对于这些模型，我们的算法具有复杂性O _p（n ^c），其中随机性是关于数据生成过程的，n是代理的数量，而c取决于战略互动的强度。我们还提供了用于在网络形成游戏中计算成对稳定和有向Nash稳定网络的算法。