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Scenario Sampling for Large Supermodular Games

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  • Bryan S. Graham
  • Andrin Pelican

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.

Suggested Citation

  • Bryan S. Graham & Andrin Pelican, 2023. "Scenario Sampling for Large Supermodular Games," NBER Working Papers 31511, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:31511
    Note: ED IO LS PE TWP
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    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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