Sharp identification regions in games

Arie Beresteanu (), Ilya Molchanov () and Francesca Molinari
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Ilya Molchanov: Institute for Fiscal Studies and University of Bern, Institute of Mathematical Statistics and Actuarial Science

No CWP15/08, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract:

We study identification in static, simultaneous move finite games of complete information, where the presence of multiple Nash equilibria may lead to partial identification of the model parameters. The identification regions for these parameters proposed in the related literature are known not to be sharp. Using the theory of random sets, we show that the sharp identification region can be obtained as the set of minimizers of the distance from the conditional distribution of game's outcomes given covariates, to the conditional Aumann expectation given covariates of a properly defined random set. This is the random set of probability distributions over action profiles given profit shifters implied by mixed strategy Nash equilibria. The sharp identification region can be approximated arbitrarily accurately through a finite number of moment inequalities based on the support function of the conditional Aumann expectation. When only pure strategy Nash equilibria are played, the sharp identification region is exactly determined by a finite number of moment inequalities. We discuss how our results can be extended to other solution concepts, such as for example correlated equilibrium or rationality and rationalizability. We show that calculating the sharp identification region using our characterization is computationally feasible. We also provide a simple algorithm which finds the set of inequalities that need to be checked in order to insure sharpness. We use examples analyzed in the literature to illustrate the gains in identification afforded by our method.

Keywords: Identification; Random Sets; Aumann Expectation; Support Function; Capacity Functional; Normal Form Games; Inequality Constraints. (search for similar items in EconPapers)
JEL-codes: C14 C72 (search for similar items in EconPapers)
Date: 2008-06-18
New Economics Papers: this item is included in nep-ecm and nep-gth
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Citations: View citations in EconPapers (24)

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