Scenario Sampling for Large Supermodular Games

Bryan Graham and Andrin Pelican

No 31511, NBER Working Papers from National Bureau of Economic Research, Inc

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(10⁴)). 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.

JEL-codes: C15 C31 C55 C7 (search for similar items in EconPapers)
Date: 2023-07
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