Scenario sampling for large supermodular games - Bryan S. Graham; Andrin Pelican (Centre for Microdata Methods and Practice (cemmap), 2023)
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.
Keywords: 330; Games; Supermodular; Importance Sampling; Simulated Maximum Likelihood (SML); Technology Adoption; Peer Effects; Strategic Network Formation; Nichtkooperatives Spiel; Simulation; Maximum-Likelihood-Schätzung; Stichprobenerhebung; Netzwerk; Soziale Gruppe; Innovationsakzeptanz; Markteintritt; Spieltheorie