Effects of core properties in four‐person games with side‐payments

This paper reports an experimental test of three competing theories of payoff allocation (the Shapley, equality, and nucleolus solutions) in n ‐person conflicts. These tests apply to decision making in group systems. Three‐hundred twenty subjects participated in four‐person cooperative, nonconstant sum, nonempty core games with side‐payments. The manipulated experimental variables included core size, location of the equality vector with respect to the core, and column difference of payoff matrices. Results show that the Shapley solution is superior to the nucleolus solution in terms of predictive accuracy. Moreover, the Shapley solution is robust to experimental treatments and thus appears to be more useful than the equality solution. Related findings indicate a high percentage of Pareto optimal outcomes (83%) and a higher frequency of outcomes falling in the core when the equality vector is located inside the core than when it is located outside. Findings are discussed in terms of core properties.