Distributing a fixed budget among decentralized intermediaries is a relevant investment problem that has led to a growing research effort in the portfolio optimization literature. While existing contributions have widely focused on the incentive mechanisms driving the actions of the decentralized intermediaries, the idea of a budget partitioning that balances fairness and efficiency has been generally overlooked. In this paper, we consider a cooperative bargaining game for the budget allocation in a class of decentralized investment problems, where financial intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. Focusing on the Nash bargaining solution and the Kalai–Smorodinsky bargaining solution, we propose a reformulation that is valid within a class of risk/disutility measures (that we call quasi-homogeneous measures). This reformulation establishes a form of duality between a complex bilevel optimization model (resulting from the extensive formulation of the equilibrium conditions) and a convex knapsack problem. In the specific case of the Nash bargaining solution, the equilibrium characterization can be established as 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 gives rise to a computational approach that facilitates its numerical solvability.