This paper reports the first cross-study competitive test of the core solution in side-payment games where the core is nonempty and nonunique (i.e., larger than a single point). The core was tested against five alternative theories including the Shapley value, the disruption nucleolus, the nucleolus, the 2-center, and the equality solution. A generalized Euclidean distance metric which indexes the average distance between an observed payoff vector and the entire set of predicted payoff vectors (Bonacich, 1979) was used as the measure of goodness-of-fit. Analysis of data assembled from six previously reported studies (encompassing a total of 1,464 observations over 56 3-person and 4-person side-payment games) showed the core to predict less accurately than the Shapley value, disruption nucleolus, and nucleolus solutions (p < 0.01). These findings are consistent with previous empirical results that show the core to have a low level of predictive accuracy in side-payment games.
1. Introduction
Since its introduction by Gillies (1953), the core has enjoyed prominence as perhaps the most important game theoretic solution concept. Core theory makes predictions regarding the resolution of n-person cooperative games, both with and without side-payments. Based on the postulates that players are not only individually and collectively rational, but also coalitionally rational, this theory holds that a proposed payoff will be accepted by players only if it leaves no coalition in a position to improve the payoffs to all members. The internal stability of core outcomes is conceptually attractive, and consequently the core has received extensive treatment in the mathematical literature (Aumann, 1961 ;Shapley and Shubik, 1966; Scarf, 1967;Maschler, Peleg, and Shapley, 1979).
Unfortunately, there appears to be no direct relationship between the core's theoretical importance and its predictive power in empirical situations. Although the core has not been extensively tested in non-side-payment games, recent experimental studies in side-payment games show the core to be Theory and Decision 15 (1983) 11-28.