Individual players in a simultaneous equation binary choice model act differently in different environments in ways that are frequently not captured by observables and a simple additive random error. This paper proposes a random coefficient specification to capture this type of heterogeneity in behaviour, and discusses nonparametric identification and estimation of the distribution of random coefficients. We establish nonparametric point identification of the joint distribution of all random coefficients, except those on the interaction effects, provided the players behave competitively in all markets. Moreover, we establish set identification of the density of the coefficients on the interaction effects, and provide additional conditions that allow to point identify this density. Since our identification strategy is constructive throughout, it allows us to construct sample counterpart estimators. We analyse their asymptotic behaviour, and illustrate their finite sample behaviour in a numerical study. Finally, we discuss several extensions, like the semiparametric case, or correlated random coefficients.

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