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.
KeywordsOptimal Design Economic Theory Game Theory Large Class Design Procedure
Unable to display preview. Download preview PDF.
- Boylan R, El-Gamal M (1993) Fictitious play: A statistical study of multiple economic experiments. Games and Economic Behavior 5: 205–222Google Scholar
- Edwards W, Lindman H, Savage L (1963) Bayesian statistical inference for psychological research. Psychological Review 70: 193–242Google Scholar
- El-Gamal M, Grether D (1995) Uncovering behavioral strategies: Likelihood based experimental data mining. Journal of the American Statistical Association. 90 (432): 1137–1145Google Scholar
- El-Gamal M, Palfrey T (1995) Vertigo: Comparing structural models of imperfect behavior in experimental games. Games and Economic Behavior 8: 322–348Google 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: 428–435Google 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: 189–200Google Scholar
- Fisher R (1950) Contributions to mathematical statistics. New York, WileyGoogle Scholar
- Harless D, Camerer C (1992) The predictive utility of generalized expected utility theories. Mimeo, University of ChicagoGoogle Scholar
- Kullback S (1959) Information theory and statistics. New York, WileyGoogle Scholar
- Lehmann L (1959) Testing statistical hypotheses. New York, WileyGoogle Scholar
- Lindley D (1957) A statistical paradox. Biometrika 44: 187–192Google Scholar
- McKelvey RD, Palfrey T (1992). An experimental study of the centipede game. Econometrica 60: 803–836Google Scholar