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This article reports a test of theories of payoff allocation in n‐person game‐theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4‐person, 2‐strategy non‐sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α‐effectiveness (von Neumann‐Morgenstern) and β‐effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the g‐imputation set was more accurate than the a‐imputation set, the β‐stable set was more accurate than the α‐stable set, and the (3‐core was more accurate than the α‐core; in other words, for each of the solutions tested, the prediction from any solution concept based on (β‐effectiveness was more accurate than the prediction from the same solution based on a‐effectiveness. Second, the β‐core was the most accurate of the six theories tested. Results are interpreted as showing that β‐effectiveness is superior to a‐effectiveness as a basis for payoff predictions in cooperative non‐sidepayment games.
Notes
This research was supported by grants SES‐8319322 and SES‐8015528 from the National Science Foundation. The authors express appreciation to Pasumarti V. Kamesam for assistance in computer programming, and to Christopher Bowen, Jennifer Brandt, Priscilla Cross, Charles Depies, Dennis Hamblin, Timothy Kasen, Christy Kinney, Greg Macheel, Connie Morris, Lauren Outland, and Kathryn Potter for assistance in data collection and analysis.