From Necklaces to Coalitions: Fair and Self-Interested Distribution of Coalition Value Calculations

2026-04-18

AI Summary

This work addresses the challenge of fairly and efficiently allocating coalition value computation tasks in characteristic function games without communication, while avoiding redundancy, load imbalance, and participation by non-members. The paper proposes a distributed algorithm, N-DCA, which establishes—for the first time—a bijection between incremental arrays and two-colored combinatorial necklaces. This enables each agent to independently determine its computation assignment based solely on its own ID and the total number of agents. The method simultaneously satisfies five key properties: communication-freeness, fairness, non-redundancy, load balance, and self-interestedness, and provides rigorous theoretical guarantees for load balancing. Empirical evaluation shows that N-DCA achieves runtime performance comparable to the DCVC algorithm under practical overheads, while offering superior memory efficiency, scalability, and robustness in ensuring self-interested behavior.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Mechanism Design

Application Category

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

Abstract

A key challenge in distributed coalition formation within characteristic function games is determining how to allocate the calculation of coalition values across a set of agents. The number of possible coalitions grows exponentially with the number of agents, and existing distributed approaches may produce uneven or redundant allocations, or assign coalitions to agents that are not themselves members. In this article, we present the \emph{Necklace-based Distributed Coalition Algorithm} (N-DCA), a communication-free algorithm in which each agent independently determines its own coalition value calculation allocation using only its identifier and the total number of agents. The approach builds on the notion of Increment Arrays (IAs), for which we develop a complete mathematical framework: equivalence classes under circular shifts, periodic IAs, and a rotated designation scheme with formal load-balance guarantees (tight bounds). We establish a bijection between canonical representative IAs and two-colour combinatorial necklaces, enabling the use of efficient necklace generation algorithms to enumerate allocations in constant amortised time. N-DCA is, to the best of our knowledge, the only distributed coalition value calculation algorithm for unrestricted characteristic function games to provably satisfy five desirable properties: no inter-agent communication, equitable allocation, no redundancy, balanced load, and self-interest. An empirical evaluation against DCVC (Rahwan and Jennings 2007) demonstrates that, although DCVC is faster by a constant factor, this difference becomes negligible under realistic characteristic-function evaluation costs, while N-DCA offers advantages in working memory, scalability, and the self-interest guarantee.

Problem

• coalition formation
• value calculation allocation
• characteristic function games
• load balancing
• self-interest

Innovation

• Necklace-based Distributed Coalition Algorithm
• Increment Arrays
• Combinatorial Necklaces
• Characteristic Function Games
• Self-interested Allocation