Go to AAMAS 2026 Conference homepageMetric Hedonic Games on the Line
Keywords: Game Theory, Coalition Formation, Hedonic Games, Clustering, Metric Distances
Abstract: Hedonic games are fundamental models for investigating the formation of coalitions among a set of strategic agents, where every agent has a certain utility for every possible coalition of agents it can be part of. To avoid the intractability of defining exponentially many utilities for all possible coalitions, many variants with succinct representations of the agents' utility functions have been devised and analyzed, e.g., modified fractional hedonic games (Monaco et al., JAAMAS 2020).
We extend this by studying a novel succinct variant that is related to modified fractional hedonic games. In our model, each agent has a fixed type-value and an agent's cost for some given coalition is based on the differences between its value and those of the other members of its coalition. This allows to model natural situations like athletes forming training groups with similar performance levels or voters that partition themselves along a political spectrum.
In particular, we investigate natural variants where an agent's cost is defined by distance thresholds, or by the maximum or average value difference to the other agents in its coalition. For these settings, we study the existence of stable states, their structure, and their quality in terms of the price of anarchy and the price of stability. Despite the simple setting with metric distances on a line, we uncover a rich landscape of models, partially with counter-intuitive behavior. Also, our focus on both Nash stability and swap stability allows us to study the influence of fixing the number and the size of the coalitions. Overall, we find that stable states always exist but that their structure and quality can vary widely.
Area: Game Theory and Economic Paradigms (GTEP)
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Submission Number: 1228
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