Cooperative bargaining games have long been used to model resource allocation and conflict resolution, but traditional solutions assumed that mediators could access agents’ utility values and gradients. This is unrealistic in emerging paradigms—such as human–AI interaction—where utilities are inaccessible or incomparable.
To address this, we proposed a bargaining algorithm in which the mediator had access only to each agent’s most preferred direction (normalized utility gradient). We proved that the algorithm is invariant to monotonic non-affine transformations, converges globally to Pareto-stationary solutions under convexity and smoothness assumptions, and satisfies symmetry and (under slightly stronger conditions) independence of irrelevant alternatives. We empirically validated our approach in multi-agent formation assignment and mediated stock-portfolio allocation.
The Thirty-Ninth Annual Conference on Neural Information Processing Systems (NeurIPS) 2025. All code for our experiments can be found here.