Causes of Stability in Dynamic Coalition Formation

TL;DR

This paper investigates how simple dynamic processes in cardinal hedonic games lead to stable coalition outcomes, highlighting the roles of resentment and appreciation in ensuring convergence under mild conditions.

Contribution

It introduces the impact of resentment and appreciation on coalition stability, demonstrating their effectiveness in driving convergence in dynamic coalition formation.

Findings

Resentful and appreciative behaviors guarantee convergence to stable outcomes.

Dynamics differ from classical models by incorporating utility changes based on history.

Both resentment and appreciation serve as strong forces promoting stability.

Abstract

We study the formation of stable outcomes via simple dynamics in cardinal hedonic games, where the utilities of agents change over time depending on the history of the coalition formation process. Specifically, we analyze situations where members of a coalition decrease their utility for a leaving agent (resent) or increase their utility for a joining agent (appreciation). We show that in contrast to classical dynamics, for resentful or appreciative agents, dynamics are guaranteed to converge under mild conditions for various stability concepts. Thereby, we establish that both resent and appreciation are strong stability-driving forces.