Nash Bargaining Partitioning in Decentralized Portfolio Management

Abstract

Understanding how to distribute a fixed budget among decentralized intermediaries is a relevant investment problem, that has been recently introduced in the context of mathematical economics and operations research. While existing contributions focus on incentive mechanisms driving the actions of the decentralized intermediaries, the idea of a budget partitioning that balances fairness and efficiency has not been part of the debate. We consider the Nash bargaining partitioning for a class of decentralized investment problems, where intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. For the equilibrium characterization, we propose a reformulation that is valid within a class of risk/disutility measures (that we call quasi-homogeneous measures). This reformulation allows the reduction of a complex bilevel optimization model (resulting from the extensive formulation of the Nash bargaining partitioning in decentralized portfolio selection) to a convex separable knapsack problem. As empirically shown using stock returns data from U.S. listed enterprises, the notion of \emph{quasi-homogeneity} not only allows to numerically characterize a budget partitioning that balances fairness and efficiency in decentralized investment, but also give rise to a computational approach that reduces its complexity and solves the vast majority of large-scale investment problems in less than a minute.