Set Identification in Models with Multiple Equilibria

By Alfred Galichon, Marc Henry. 2011

192 citations recorded by the source corpus.

We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and efficient and easily implementable combinatorial methods are described to check them. In all normal form games, the identified set is characterized in terms of the value of a submodular or convex optimization program. Efficient algorithms are then given and compared to check inclusion of a parameter in this identified set. The latter are illustrated with family bargaining games and oligopoly entry games. Copyright 2011, Oxford University Press.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/4e16325d631ab0772df8d81f02ad52a0e3347bc8

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Citations in the corpus

Inference on Causal and Structural Parameters using Many Moment Inequalities (2013, background): “In some special settings, such as those studied in Theorem 4 of Galichon and Henry (2011), the number of moment inequalities can be dramatically reduced without blowing up the identified set (and so without any subjective choice).”
Generalized instrumental inequalities: testing the instrumental variable independence assumption (2020, background): “Theorem 1 of Galichon and Henry (2011) allows to characterize all the restrictions imposed by the potential outcome and the JSI assumption on the distribution of unobservables pY0, Y1q and the distribution of the observables pY,D,Zq.”
Discrete games with flexible information structures: an application to local grocery markets (2014, unknown): “1 Electronic copy available at: http://ssrn.com/abstract=1859643”
Econometric Analysis of Games with Multiple Equilibria (2012, background): “Grieco (2012), for example, extends it to a game of incomplete information where some variables are publicly observed by the participants but not by the econometrician.”
Testing Many Moment Inequalities (2013, background): “Other prominent examples leading to many moment inequalities are developed in Beresteanu, Molchanov, and Molinari (2011), Galichon and Henry (2011), and Chesher, Rosen, and Smolinski (2013), where moment inequalities are used to provide sharp identification regions for parameters in partially…”
TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, methodology): “4 of Giné, Mason, and Zaitsev (2003), it is worth noting that in contrast to Lemma 2.”
Identification of Social Interactions (2011, unknown): “…implementable choice structure is implemented by assuming the difference between the payoffs for the two choices is additive in 43See Berry and Tamer (2006) for an overview, and Beresteanu, Molchanov, and Molinari (2008) and Galichon and Henry (2008) for recent advances in partial identification.”
Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information (2010, unknown): “For example, if agents have an incentive to coordinate on a particular action then an exogenous intervention that induces a subset of participants to choose a certain action should at the same time also incentivize Recent work by Grieco (2010) studies a class of games with flexible information struc”