Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability

This paper proves a nonparametric identification result for a stochastic dynamic discrete choice game of incomplete information. The joint distribution of the private information and the stage game payoffs of the players are both assumed unknown for the econometrician and the private information across alternatives is allowed to have different distributions and be dependent. This setup poses a circularity problem in the identification strategy that has not been solved for dynamic games. This paper proposes a solution through exclusion restrictions and implied properties of the unknown functions. Under the assumptions that the distribution of the private shocks for the outside option is known and the outside option’s shocks are independent of other shocks, the results jointly identify the stage game payoffs and the joint distribution of the private information.