TY - CHAP
T1 - Partnership's profit sharing
T2 - Linear and nonlinear contracts
AU - Gerchak, Yigal
AU - Khmelnitsky, Eugene
N1 - Publisher Copyright:
© 2020 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
PY - 2019/10/14
Y1 - 2019/10/14
N2 - Suppose that one party proposes to another a contract for sharing an uncertain profit which maximizes the former's expected utility, with respect to its beliefs, subject to a constraint on the latter's expected utility, with respect to the latter's beliefs. It turns out that the optimal contract, which we find, can be nonmonotone, as well as nonlinear, in the realized profit. To avoid the implausible lack of monotonicity, we formulate and solve a model constrained to have monotone increasing profits for both partners. If beliefs are identical, the (unconstrained) contract is shown to be monotone, and under certain conditions, linear. That might explain one famous contract from the history of jazz. If the other party can be assumed risk neutral, the linear contract reduces to the former receiving a constant amount, and the latter the residual net profit, as in the case of another famous contract from the history of jazz. Since in the type of partnerships, we have in mind the partners are always motivated to exert high effort due to other factors like reputation, our setting has no moral hazard or adverse selection, and the partnerships do not involve a large initial investment.
AB - Suppose that one party proposes to another a contract for sharing an uncertain profit which maximizes the former's expected utility, with respect to its beliefs, subject to a constraint on the latter's expected utility, with respect to the latter's beliefs. It turns out that the optimal contract, which we find, can be nonmonotone, as well as nonlinear, in the realized profit. To avoid the implausible lack of monotonicity, we formulate and solve a model constrained to have monotone increasing profits for both partners. If beliefs are identical, the (unconstrained) contract is shown to be monotone, and under certain conditions, linear. That might explain one famous contract from the history of jazz. If the other party can be assumed risk neutral, the linear contract reduces to the former receiving a constant amount, and the latter the residual net profit, as in the case of another famous contract from the history of jazz. Since in the type of partnerships, we have in mind the partners are always motivated to exert high effort due to other factors like reputation, our setting has no moral hazard or adverse selection, and the partnerships do not involve a large initial investment.
KW - Contracts
KW - Jazz history
KW - Optimal control
KW - Partnerships
KW - Risk-aversion
UR - http://www.scopus.com/inward/record.url?scp=85122225847&partnerID=8YFLogxK
U2 - 10.1142/9789811202018_0019
DO - 10.1142/9789811202018_0019
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???
AN - SCOPUS:85122225847
SN - 9789811202001
SP - 419
EP - 436
BT - Game Theoretic Analysis
PB - World Scientific Publishing Co. Pte Ltd
ER -