Econometric analysis of games with multiple equilibria

Abstract

This article reviews the recent literature on the econometric analysis of games where multiple solutions are possible. Multiplicity does not necessarily preclude the estimation of a particular model (and in certain cases even improves its identification), but ignoring it can lead to misspecifications. The survey starts with a general characterization of structural models that highlights how multiplicity a↵ects the classical paradigm.Because the information structure is an important guide to identification and estimation strategies, I discuss games of complete and incomplete information separately.Whereas many of the techniques discussed in the article can be transported across different information environments, some of them are specific to particular models. I also survey models of social interactions in a di↵erent section. I close with a brief discussion of post-estimation issues and research prospects.

Treatment Effect Models with Strategic Interaction in Treatment Decisions

“…Based on this, we can improve the estimation efficiency, as discussed in Remark 4.2. This advantage of over-identification would be viewed as reminiscent of the findings in the game econometrics literature (e.g., de Paula and Tang, 2012;de Paula, 2013). Intuitively, when multiple equilibria between D = (0, 0) and (1, 1) exist because of complementarity, the data exhibit a positive correlation between D j and D −j , and this provides more chances of identifying m (0,0) (x, p 1 , p 2 ) and m (1,1) (x, p 1 , p 2 ) than in the other two cases.…”

“…To handle the incompleteness problem, there are essentially three approaches in the game econometrics literature (see de Paula (2013) for an excellent survey on this topic). The first approach is to focus only on the outcomes that can occur as unique equilibria (e.g., Bresnahan and Reiss, 1990;Berry, 1992).…”

Econometric Models of Network Formation

“…The approach above would produce on bounds on δ corresponding to the probability that a particular network is pairwise stable (though possibly not unique) (upper bound) and the probability that it is the unique pairwise stable network (lower bound). In the figure above (which does not comprise the whole space for s), those bounds for the network {12, 13} would be P( 12 , 13 ≥ 0) ≥ P({12, 13}) ≥ P( 12 , 13 ≥ δ/(1 − δ)), 21 For additional strategies to handle the multiplicity problem, see de Paula (2013).…”

Two-step estimation of network-formation models with incomplete information

“…we typically require degeneracy in order to ensure that in the first stage, we nonparametrically estimate choice probabilities, rather than mixtures of choice probabilities (Paula, 2013). This is unnecessary under large-market asymptotics, since we need not pool observations across markets.…”