Nash Bargaining Partitioning in Decentralized Portfolio Management

In the context of decentralized portfolio optimization, understanding how to distribute a fixed budget among decentralized intermediaries is a relevant investment problem, that has been recently introduced in the mathematical economics literature. 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) and allows the reduction of a complex bilevel optimization model to a convex separable knapsack problem. As empirically shown using stock returns data from U.S. listed enterprises, the notion of 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 computationally efficient approach solving the vast majority of large-scale investment problems in less than a minute