Visualizing Coalition Formation: From Hedonic Games to Image Segmentation

TL;DR

This paper introduces a novel approach to analyze coalition formation in hedonic games using image segmentation as a diagnostic tool, revealing how parameters influence equilibrium structures and fragmentation.

Contribution

It bridges multi-agent coalition formation with image segmentation, quantifying how mechanism parameters affect equilibrium fragmentation and boundary structures.

Findings

Transition from cohesive to fragmented equilibria observed

Relation established between multi-coalition and binary protocols

Excessive fragmentation leads to intrinsic failure

Abstract

We propose image segmentation as a visual diagnostic testbed for coalition formation in hedonic games. Modeling pixels as agents on a graph, we study how a granularization parameter shapes equilibrium fragmentation and boundary structure. On the Weizmann single-object benchmark, we relate multi-coalition equilibria to binary protocols by measuring whether the converged coalitions overlap with a foreground ground-truth. We observe transitions from cohesive to fragmented yet recoverable equilibria, and finally to intrinsic failure under excessive fragmentation. Our core contribution links multi-agent systems with image segmentation by quantifying the impact of mechanism design parameters on equilibrium structures.