Scenario Sampling for Large Supermodular Games

Bryan S. Graham; Andrin Pelican

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arXiv · 2307.11857

Scenario Sampling for Large Supermodular Games

Bryan S. Graham·Andrin Pelican

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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.

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econ.EM econ.TH math.ST stat.CO stat.TH

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Bryan S. Graham, Andrin Pelican. 2023-07-21. Scenario Sampling for Large Supermodular Games. https://arxiv.org/abs/2307.11857

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