On the Formation of Steady Coalitions

TL;DR

This paper analyzes the internal dynamics of coalition formation in cooperative games, providing a characterization of when the grand coalition cannot form due to conflicting coalition demands, using new polyhedral tools.

Contribution

It introduces a novel characterization of coalition formation impossibility and develops new polyhedral tools applicable in cooperative game theory.

Findings

Characterization of conditions preventing grand coalition formation.

Development of new polyhedral tools for cooperative game analysis.

Insights into coalition dynamics and payoff negotiations.

Abstract

This paper studies the formation of the grand coalition of a cooperative game by investigating its possible internal dynamics. Each coalition is capable of forcing all players to reconsider the current state of the game when it does not provide sufficient payoff. Different coalitions may ask for contradictory evolutions, leading to the impossibility of the grand coalition forming. In this paper, we give a characterization of the impossibility, for a given state, of finding a new state dominating the previous one such that each aggrieved coalition has a satisfactory payoff. To do so, we develop new polyhedral tools related to a new family of polyhedra, appearing in numerous situations in cooperative game theory.