Finding Fair Allocations for the Coalition Problem with Constraints

Fair allocation of payoffs among cooperating players who can form various coalitions of differing utilities is the classic game theoretic “coalition problem.” Shapley’s value is perhaps the most famous fairness criterion. In this paper, a new allocation principle is proposed based on constraints. Initially constraints are defined by the coalition payoffs, in the standard way. The algorithm proceeds by “tightening” the constraints in a fair manner until the solution space is sufficiently small. An arbitrary boundary point is then chosen as the “fair” allocation. Our technique has been implemented in the constraint programming language CLP(R) and evaluated against Shapley values for various benchmark problems. We show how our method is related to Shapley values, some empirical tests and describe an application to bond swaps.

• Type: Conference
• Year: 1999
• Where: ICLP
• Authors: Evan Tick, Roland H. C. Yap, Michael J. Maher
• Keywords: Automated Reasoning, Fair Allocation, ICLP 1999, Shapley Values, Shapley’s Value