Noise Robust Core-Stable Coalitions of Hedonic Games
Prashant Trivedi, Nandyala Hemachandra

TL;DR
This paper investigates the robustness of core-stable coalition partitions in hedonic games under noisy preferences, providing probabilistic bounds and regimes where stability persists despite noise, with exact solutions for two-agent cases.
Contribution
It introduces a multiplicative noise model for coalition preferences, derives explicit prediction probabilities, and characterizes noise regimes ensuring core stability in noisy and noise-free settings.
Findings
Prediction probability depends on an agreement event.
Noise regimes for robustness are non-convex sets.
Exact solutions provided for 2-agent hedonic games.
Abstract
We consider the coalition formation games with an additional component, `noisy preferences'. Moreover, such noisy preferences are available only for a sample of coalitions. We propose a multiplicative noise model and obtain the prediction probability, defined as the probability that the estimated PAC core-stable partition of the noisy game is also PAC core-stable for the unknown noise-free game. This prediction probability depends on the probability of a combinatorial construct called an `agreement event'. We explicitly obtain the agreement probability for agent noisy game with l\geq 2 support noise distribution. For a user-given satisfaction value on this probability, we identify the noise regimes for which an estimated partition is noise robust; that is, it is PAC core-stable in both noisy and noise-free games. We obtain similar robustness results when the estimated partition is…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Game Theory and Applications
