Dynamics of Profit-Sharing Games

TL;DR

This paper analyzes how selfish agents form coalitions with convex profit functions under bounded rationality, proposing profit-sharing schemes and studying the resulting dynamics, equilibria, and efficiency bounds.

Contribution

It introduces three profit-sharing schemes based on marginal utility for coalition formation and analyzes their dynamic properties and efficiency bounds under bounded rationality.

Findings

Bounded rationality leads to convergence to approximate equilibria.

Proposed schemes have bounded price of anarchy and stability.

Coalition dynamics can be analyzed within polynomial time.

Abstract

An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings where each team's profit is given by a convex function, and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.