Skip to main content

Economical experiments: Bayesian efficient experimental design


We propose and implement a Bayesian optimal design procedure. Our procedure takes as its primitives a class of parametric models of strategic behavior, a class of games (experimental designs), and priors on the behavioral parameters. We select the experimental design that maximizes the information from the experiment. We sequentially sample with the given design and models until only one of the models has viable posterior odds. A model which has low posterior odds in a small collection of models will have an even lower posterior odds when compared to a larger class, and hence we can dismiss it. The procedure can be used sequentially by introducing new models and comparing them to the models that survived earlier rounds of experiments. The emphasis is not on running as many experiments as possible, but rather on choosing experimental designs to distinguish between models in the shortest possible time period. We illustrate this procedure with a simple experimental game with one-sided incomplete information.

This is a preview of subscription content, access via your institution.


  • Boylan R, El-Gamal M (1993) Fictitious play: A statistical study of multiple economic experiments. Games and Economic Behavior 5: 205–222

    Google Scholar 

  • Edwards W, Lindman H, Savage L (1963) Bayesian statistical inference for psychological research. Psychological Review 70: 193–242

    Google Scholar 

  • El-Gamal M, Grether D (1995) Uncovering behavioral strategies: Likelihood based experimental data mining. Journal of the American Statistical Association. 90 (432): 1137–1145

    Google Scholar 

  • El-Gamal M, Palfrey T (1995) Vertigo: Comparing structural models of imperfect behavior in experimental games. Games and Economic Behavior 8: 322–348

    Google Scholar 

  • El-Gamal M, McKelvey R, Palfrey T (1993a) A Bayesian sequential experimental study of learning in games. Journal of the American Statistical Association 88: 428–435

    Google Scholar 

  • El-Gamal M, McKelvey R, Palfrey T (1993b) Computational issues in the statistical design and analysis of experimental games. International Journal of Supercomputer Applications 7/3: 189–200

    Google Scholar 

  • Fisher R (1950) Contributions to mathematical statistics. New York, Wiley

  • Harless D, Camerer C (1992) The predictive utility of generalized expected utility theories. Mimeo, University of Chicago

  • Kullback S (1959) Information theory and statistics. New York, Wiley

    Google Scholar 

  • Lehmann L (1959) Testing statistical hypotheses. New York, Wiley

    Google Scholar 

  • Lindley D (1957) A statistical paradox. Biometrika 44: 187–192

    Google Scholar 

  • McKelvey RD, Palfrey T (1992). An experimental study of the centipede game. Econometrica 60: 803–836

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

We acknowledge the financial support from NSF grant #SES-9223701 to the California Institute of Technology. We also acknowledge the research assistance of Eugene Grayver who wrote the software for the experiments.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

El-Gamal, M.A., Palfrey, T.R. Economical experiments: Bayesian efficient experimental design. Int J Game Theory 25, 495–517 (1996).

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI:


  • Optimal Design
  • Economic Theory
  • Game Theory
  • Large Class
  • Design Procedure