Probabilistically robust stabilizing allocations in uncertain coalitional games

TL;DR

This paper introduces a probabilistic framework for ensuring stable allocations in uncertain multi-agent coalitional games, providing distribution-free guarantees and a randomized relaxation approach when the core is empty.

Contribution

It proposes a novel probabilistic stability guarantee method and a randomized core relaxation for uncertain coalitional games, extending stability analysis to cases with an empty core.

Findings

Distribution-free stability guarantees established.

A randomized core relaxation method proposed.

Numerical experiments validate theoretical results.

Abstract

In this paper we consider multi-agent coalitional games with uncertain value functions for which we establish distribution-free guarantees on the probability of allocation stability, i.e., agents do not have incentives to defect from the grand coalition to form subcoalitions for unseen realizations of the uncertain parameter. In case the set of stable allocations, the so called core of the game, is empty, we propose a randomized relaxation of the core. We then show that those allocations that belong to this relaxed set can be accompanied by stability guarantees in a probably approximately correct fashion. Finally, numerical experiments corroborate our theoretical findings.