On the non-identification of counterfactuals in dynamic discrete games

In single-agent dynamic discrete choice models, counterfactual behavior is identified for some (but not all) counterfactuals despite the fact that the models themselves are under-identified. We review recent results on the identification of counterfactuals in dynamic discrete choice settings. When it comes to dynamic discrete games, we argue that counterfactuals are not identified, even when analogous counterfactuals of single-agent models are identified. Using the example of a duopoly entry game, we explain why strategic considerations undermine the identification of counterfactual equilibria in dynamic games.