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Title:Sharp identification regions in games PDF Logo
Authors:Beresteanu, Arie
Molchanov, Ilya
Molinari, Francesca
Issue Date:2008
Series/Report no.:cemmap working paper CWP15/08
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.
Subjects:Identification
Random Sets
Aumann Expectation
Support Function
Capacity Functional
Normal Form Games
Inequality Constraints
JEL:C14
C72
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2008.1508
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

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