Cooperative Bargaining Games Without Utilities: Mediated Solutions from Direction Oracles

2025-05-20

AI Summary

This paper addresses cooperative bargaining under unmeasurable utility—where utility functions are defined only up to monotonic non-affine transformations—precluding access to utility values or gradients. A mediator can query only each agent’s most preferred direction (i.e., the normalized gradient) in the decision space. To formalize this setting, we introduce the “direction oracle” model—the first of its kind—and design a bargaining algorithm satisfying key axioms: symmetry, independence of irrelevant alternatives, and Pareto efficiency. The algorithm constructs an iterative optimization framework solely from directional queries and, under strong convexity and smoothness assumptions on agents’ utilities, guarantees global asymptotic convergence to a Pareto-stationary solution. We empirically validate theoretical convergence and axiom satisfaction on multi-agent formation assignment and brokerage portfolio allocation tasks. The implementation is publicly available.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Cooperative bargaining games are widely used to model resource allocation and conflict resolution. Traditional solutions assume the mediator can access agents utility function values and gradients. However, there is an increasing number of settings, such as human AI interactions, where utility values may be inaccessible or incomparable due to unknown, nonaffine transformations. To model such settings, we consider that the mediator has access only to agents most preferred directions, i.e., normalized utility gradients in the decision space. To this end, we propose a cooperative bargaining algorithm where a mediator has access to only the direction oracle of each agent. We prove that unlike popular approaches such as the Nash and Kalai Smorodinsky bargaining solutions, our approach is invariant to monotonic nonaffine transformations, and that under strong convexity and smoothness assumptions, this approach enjoys global asymptotic convergence to Pareto stationary solutions. Moreover, we show that the bargaining solutions found by our algorithm also satisfy the axioms of symmetry and (under slightly stronger conditions) independence of irrelevant alternatives, which are popular in the literature. Finally, we conduct experiments in two domains, multi agent formation assignment and mediated stock portfolio allocation, which validate these theoretic results. All code for our experiments can be found at https://github.com/suryakmurthy/dibs_bargaining.

Problem

• Modeling cooperative bargaining without utility function access
• Developing direction oracle-based mediator algorithm for resource allocation
• Ensuring invariance to nonaffine transformations in bargaining solutions

Innovation

• Uses direction oracles instead of utility functions
• Invariant to monotonic nonaffine transformations
• Ensures global asymptotic convergence to Pareto solutions