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 that respects 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.
References
Binmore K, Rubinstein A, Wolinsky A (1986) The Nash bargaining solution in economic modelling. Rand J Econ 17(2):176–188
Borch K (1962) Equilibrium in a reinsurance market. Econometrica 30(3):424–444
Brousseau E, Glachant J-M (2002) The economics of contracts: theory and applications. Press, Cambridge University
Dubra J (2001) An asymmetric Kalai-Smorodinsky solution. Econ Lett 73:131–136
Friedman JW (1986) Game theory with applications to economics. Oxford University Press, Oxford, UK
Gerchak Y, Khmelnitsky E (2019a) Partnership’s profit sharing: linear and non-linear contracts. Int Game Theory Rev 21. https://doi.org/10.1142/S0219198919400085
Gerchak Y, Khmelnitsky E (2019b) Bargaining over shares of uncertain future profits. EURO J Decis Processes 7:55–68
Gerchak, Y, Khmelnitsky E (2019c) Profit sharing via the Kalai-Smorodinsky solution, working paper
Hartl RF, Sethi SP, Vickson RG (1995) A survey of the maximum principles for optimal control problems with state constraints. SIAM Rev 37:181–218
Kadan O, Swinkels JM (2013) On the moral hazard problem without the first-order approach. J Econ Theory 148(6):2313–2343
Kalai E (1977) Nonsymmetric Nash solutions and replications of 2-person bargaining. Int J Game Theory 6(3):129–133
Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problem. Econometrica 43(3):513–518
Khmelnitsky E (2002) A combinatorial, graph-based solution method for a class of continuous-time optimal control problems. Math Oper Res 27:312–325
Kihlstrom R, Roth AE, Schmeidler D (1981) Risk aversion and solutions to Nash’s bargaining problem. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. Elsevier North-Holland Publishing Company, Amsterdam, pp 65–71
Levin J, Tadelis S (2005) Profit sharing and the role of professional partnerships. Q J Econ 120(1):131–171
Muthoo A (1999) Bargaining theory with applications. Cambridge University Press, Cambridge
Nash J (1950) The bargaining problem. Econometrica 21(1):128–140
Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50(1):97–109
Ward GC, Burns K (2000) Jazz: a history of America’s Music. Knopf. Random House Inc., New York
Weinstock R (1974) Calculus of variations with applications to physics and engineering. Dover Publications, New York
Wilson R (1968) The theory of syndicates. Econometrica 36(1):119–132
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this entry
Cite this entry
Gerchak, Y., Khmelnitsky, E. (2020). Sharing Profit and Risk in a Partnership. In: Kilgour, D., Eden, C. (eds) Handbook of Group Decision and Negotiation. Springer, Cham. https://doi.org/10.1007/978-3-030-12051-1_46-1
Download citation
DOI: https://doi.org/10.1007/978-3-030-12051-1_46-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12051-1
Online ISBN: 978-3-030-12051-1
eBook Packages: Springer Reference Behavioral Science and PsychologyReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences