The Raiffa–Kalai–Smorodinsky Solution as a Mechanism for Dividing the Uncertain Future Profit of a Partnership

Yigal Gerchak and Eugene Khmelnitsky ()
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Yigal Gerchak: Department of Industrial Engineering, Tel Aviv University, Tel-Aviv 69978, Israel
Eugene Khmelnitsky: Department of Industrial Engineering, Tel Aviv University, Tel-Aviv 69978, Israel

Games, 2025, vol. 16, issue 3, 1-13

Abstract: Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa–Kalai–Smorodinsky (K-S) solution, which is the intersection point of the feasible region’s boundary and the line connecting the disagreement and ideal points. It is the only function which satisfies invariance to linear transformations, symmetry, strong Pareto optimality, and monotonicity. We formulate the general problem of designing a contract which divides uncertain future profit between the partners and determines shares of each partner. We first focus on linear and, later, non-linear contracts between two partners, providing analytical and numerical solutions for various special cases in terms of the utility functions of the partners, their beliefs, and the disagreement point. We then generalize the analysis to any number of partners. We also consider a contract which is partially based on the parties’ financial contribution to the partnership, which have a positive impact on profit. Finally, we address asymmetric K-S solutions. K-S solutions are seen to be a useful predictor of the outcome of negotiations, similar to Nash’s bargaining solution.

Keywords: linear and non-linear contract; risk-aversion; bargaining; profit sharing (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
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