Risk-Averse Bargaining in a Stochastic Optimization Context
研究了风险厌恶代理人间公平分配随机利润的讨价还价问题，提出基于公理的求解方法，并证明最优解可表示为期权合约组合，对管理决策有指导意义。
Problem definition: Bargaining situations are ubiquitous in economics and management. We consider the problem of bargaining for a fair ex ante distribution of random profits arising from a cooperative effort of a fixed set of risk-averse agents. Our approach integrates optimal managerial decision making into bargaining situations with random outcomes and explicitly models the impact of risk aversion. The proposed solution rests on a firm axiomatic foundation and yet allows to compute concrete bargaining solutions for a wide range of practically relevant problems. Methodology/results: We model risk preferences using coherent acceptability functionals and base our bargaining solution on a set of axioms that can be considered a natural extension of Nash bargaining to our setting. We show that the proposed axioms fully characterize a bargaining solution, which can be efficiently computed by solving a stochastic optimization problem. We characterize special cases where random payoffs of players are simple functions of overall project profit. In particular, we show that, for players with distortion risk functionals, the optimal bargaining solution can be represented by an exchange of standard options contracts with the project profit as the underlying asset. We illustrate the concepts in the paper with a detailed example of risk-averse households that jointly invest into a solar plant. Managerial implications: We demonstrate that there is no conflict of interest between players about management decisions and that risk aversion facilitates cooperation. Furthermore, our results on the structure of optimal contracts as a basket of option contracts provides valuable guidance for negotiators. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.1076 .