This paper introduces a simulation algorithm for evaluating the log-likelihood function of a large supermodular binary-action game. Covered examples include (certain types of) peer effect, technology adoption, strategic network formation, and multi-market entry games. More generally, the algorithm facilitates simulated maximum likelihood (SML) estimation of games with large numbers of players, $T$, and/or many binary actions per player, $M$ (e.g., games with tens of thousands of strategic actions, $TM=O(10^4)$). In such cases the likelihood of the observed pure strategy combination is typically (i) very small and (ii) a $TM$-fold integral who region of integration has a complicated geometry. Direct numerical integration, as well as accept-reject Monte Carlo integration, are computationally impractical in such settings. In contrast, we introduce a novel importance sampling algorithm which allows for accurate likelihood simulation with modest numbers of simulation draws.

翻译：本文提出了一种用于评估大规模超模二元行动博弈对数似然函数的模拟算法。涵盖的示例包括（特定类型的）同伴效应、技术采用、策略性网络形成以及多市场进入博弈。更一般地，该算法促进了具有大量参与者$T$和/或每个参与者具有多个二元行动$M$的博弈（例如，具有数万个策略性行动$TM=O(10^4)$的博弈）的模拟极大似然（SML）估计。在此类情形下，观测到的纯策略组合的似然通常（i）非常小，且（ii）是一个积分区域具有复杂几何结构的$TM$重积分。在这些设定下，直接数值积分以及接受-拒绝蒙特卡洛积分在计算上是不切实际的。相比之下，我们引入了一种新颖的重要性采样算法，该算法允许在模拟抽取次数适中的情况下进行精确的似然模拟。