Sharing Profit and Risk in a Partnership

Abstract

The setting up of a new partnership involves negotiation. Would-be partners must agree on a scheme for dividing uncertain future profits (or losses). We consider partnerships of two or more partners where initial investment is equal, and the negotiated division depends only on the partners’ attitudes toward risk, their beliefs concerning future profit, and their alternatives (i.e., the disagreement point). We propose several schemes. First, an asymmetric approach starts with one party making a decision that maximizes its expected utility while respecting the other’s individual rationality. The other two schemes are symmetric and based on negotiation; they rely on the Nash bargaining solution and the Kalai-Smorodinsky bargaining solution, respectively, and their unbalanced versions. We provide general definitions and highlight some special cases.