Scenario Sampling for Large Supermodular Games

Author:

Bryan S. Graham, Andrin Pelican

Keyword:

Economics, Econometrics, Econometrics (econ.EM), Theoretical Economics (econ.TH), Statistics Theory (math.ST), Computation (stat.CO)

journal:

date:

2023-07-20 16:00:00

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.

PDF: Scenario Sampling for Large Supermodular Games.pdf