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A comparison of the alpha- and beta-characteristic functions in cooperative non-sidepayment \(n\)-person games. (English) Zbl 0567.90100
Summary: 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 \(\alpha\)-effectiveness (von Neumann-Morgenstern) and \(\beta\)-effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the \(\beta\)-imputation set was more accurate than the \(\alpha\)-imputation set, the \(\beta\)-stable set was more accurate than the \(\alpha\)-stable set, and the \(\beta\)-core was more accurate than the \(\alpha\)-core; in other words, for each of the solutions tested, the prediction from any solution concept based on \(\beta\)-effectiveness was more accurate than the prediction from the same solution based on \(\alpha\)-effectiveness. Second, the \(\beta\)-core was the most accurate of the six theories tested. Results are interpreted as showing that \(\beta\)-effectiveness is superior to \(\alpha\)-effectiveness as a basis for payoff predictions in cooperative non-sidepayment games.

MSC:
91A12 Cooperative games
91A90 Experimental studies
91E99 Mathematical psychology
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