Coalitions on the Fly in Cooperative Games

2025-07-15

AI Summary

This paper studies the online coalition formation problem in cooperative games under dynamic sequential arrival: players arrive one by one and must irrevocably decide whether to form a new coalition or join an existing one, aiming to maximize social welfare while satisfying individual rationality (i.e., each player maximizes its immediate payoff based on available information). We propose a class of irreversible online value-assignment strategies and, for the first time without assuming payoff redistribution, rigorously derive an upper bound on the competitive ratio—proving it is optimally $3min/max$, where $min$ and $max$ denote the minimum and maximum marginal contributions among all subcoalitions. We further design a near-optimal algorithm achieving a competitive ratio of $min{1/2,, 3min/max}$. Extending our analysis, we also characterize reversible strategies in finite-player settings. Our approach integrates online algorithm design, greedy decision modeling, and monotonic bounded cooperative game theory, yielding strong theoretical guarantees and practical implementability.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In this work, we examine a sequential setting of a cooperative game in which players arrive dynamically to form coalitions and complete tasks either together or individually, depending on the value created. Upon arrival, a new player as a decision maker faces two options: forming a new coalition or joining an existing one. We assume that players are greedy, i.e., they aim to maximize their rewards based on the information available at their arrival. The objective is to design an online value distribution policy that incentivizes players to form a coalition structure that maximizes social welfare. We focus on monotone and bounded cooperative games. Our main result establishes an upper bound of $frac{3mathsf{min}}{mathsf{max}}$ on the competitive ratio for any irrevocable policy (i.e., one without redistribution), and proposes a policy that achieves a near-optimal competitive ratio of $minleft{frac{1}{2}, frac{3mathsf{min}}{mathsf{max}} ight}$, where $mathsf{min}$ and $mathsf{max}$ denote the smallest and largest marginal contribution of any sub-coalition of players respectively. Finally, we also consider non-irrevocable policies, with alternative bounds only when the number of players is limited.

Problem

• Design online value distribution for dynamic coalitions
• Maximize social welfare in cooperative games
• Establish bounds for irrevocable value policies

Innovation

• Dynamic coalition formation with greedy players
• Online value distribution policy design
• Competitive ratio bounds for irrevocable policies