Learning and equilibrium as useful approximations: Accuracy of prediction on randomly selected constant sum games

• Published in: Economic theory Vol. 33; no. 1; pp. 29 - 51
• Main Authors: Erev, Ido, Roth, Alvin E., Slonim, Robert L., Barron, Greg
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.10.2007; Springer Nature B.V
• Subjects: Approximation; Behavioural economics; Economic behaviour; Economic models; Economists; Equilibrium; Expected utility; Experiments; Game theory; Games; Games of strategy; Hypotheses; Learning; Modeling; Nash equilibrium; Observational learning; Outcomes of education; Parametric models; Psychologists; Statistical variance; Studies; SYMPOSIUM
• ISSN: 0938-2259; 1432-0479
• DOI: 10.1007/s00199-007-0214-y

There is a good deal of miscommunication among experimenters and theorists about how to evaluate a theory that can be rejected by sufficient data, but may nevertheless be a useful approximation. A standard experimental design reports whether a general theory can be rejected on an informative test case. This paper, in contrast, reports an experiment designed to meaningfully pose the question: "how good an approximation does a theory provide on average." It focuses on a class of randomly selected games, and estimates how many pairs of experimental subjects would have to be observed playing a previously unexamined game before the mean of the experimental observations would provide a better prediction than the theory about the behavior of a new pair of subjects playing this game. We call this quantity the model's equivalent number of observations, and explore its properties.