Advanced Search
MyIDEAS: Login

Sharp identification regions in games

Contents:

Author Info

  • Arie Beresteanu

    (Institute for Fiscal Studies and Duke)

  • Ilya Molchanov
  • Francesca Molinari

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://cemmap.ifs.org.uk/wps/cwp1508.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP15/08.

as in new window
Length:
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:ifs:cemmap:15/08

Contact details of provider:
Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Email:
Web page: http://cemmap.ifs.org.uk
More information through EDIRC

Order Information:
Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
Email:

Related research

Keywords: Identification; Random Sets; Aumann Expectation; Support Function; Capacity Functional; Normal Form Games; Inequality Constraints.;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Validity of Subsampling and "Plug-in Asymptotic" Inference for Parameters Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1620, Cowles Foundation for Research in Economics, Yale University.
  2. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
  3. Michael J. Mazzeo, 2002. "Product Choice and Oligopoly Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 221-242, Summer.
  4. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
  5. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  6. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
  7. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, 07.
  8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  9. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, 09.
  10. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  11. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
  12. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Donald W.K. Andrews & Gustavo Soares, 2007. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Cowles Foundation Discussion Papers 1631, Cowles Foundation for Research in Economics, Yale University.
  14. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Arie Beresteanu, 2009. "Sharp Identification Regions in Models with Convex Predictions: Games, Individual Choice, and Incomplete Data," Working Papers 428, University of Pittsburgh, Department of Economics, revised Sep 2010.
  2. Giorgio Topa & Elizabeth Setren & Meta Brown, 2011. "Do Referrals Lead to Better Matches? Evidence from a Firm's Employee," 2011 Meeting Papers 711, Society for Economic Dynamics.
  3. Donald W.K. Andrews & Panle Jia, 2008. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Cowles Foundation Discussion Papers 1676, Cowles Foundation for Research in Economics, Yale University.
  4. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," 2004 Meeting Papers 52, Society for Economic Dynamics.
  5. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
  6. Steven N. Durlauf & Yannis M. Ioannides, 2009. "Social Interactions," Discussion Papers Series, Department of Economics, Tufts University 0739, Department of Economics, Tufts University.
  7. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.
  8. Donald W.K. Andrews & Xiaoxia Shi, 2010. "Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1761R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2011.
  9. Marc Henry & Ismael Mourifi�, 2012. "Sharp Bounds in the Binary Roy Model," CIRJE F-Series CIRJE-F-835, CIRJE, Faculty of Economics, University of Tokyo.
  10. Alberto Bisin & Andrea Moro & Giorgio Topa, 2011. "The Empirical Content of Models with Multiple Equilibria in Economies with Social Interactions," NBER Working Papers 17196, National Bureau of Economic Research, Inc.
  11. J. Stoye, 2009. "Charles F. Manski, Identification for Prediction and Decision (Harvard University Press 2007)," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 857-862.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:15/08

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Stephanie Seavers).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.