Scenario Sampling for Large Supermodular Games

TL;DR

This paper presents a novel importance sampling algorithm that efficiently evaluates the likelihood function of large supermodular binary-action games, enabling practical maximum likelihood estimation in complex, high-dimensional strategic settings.

Contribution

It introduces a new simulation algorithm for likelihood evaluation in large supermodular games, overcoming computational challenges of traditional methods.

Findings

Efficient likelihood simulation with modest simulation draws.

Applicable to large-scale games with thousands of strategic actions.

Facilitates maximum likelihood estimation in complex strategic models.

Abstract

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.