Full Cooperation in Repeated Multi-Player Games on Hypergraphs

2025-04-15

AI Summary

This paper investigates the evolutionary mechanisms enabling “full cooperation”—where all players exhaust their initial endowments to achieve collective optimality—in repeated multiplayer public goods games (PGGs) on hypergraphs. Addressing the coupled effects of individual heterogeneity (e.g., endowments, productivity, cross-game resource allocation) and complex hypergraph interaction topology, we establish the first theoretical framework for repeated multiplayer PGGs on hypergraphs, integrating Nash equilibrium analysis with parametric modeling. We find that uniform endowment allocation—common in classical models—paradoxically suppresses cooperation in heterogeneous hypergraphs. To address this, we propose a dual-path optimization paradigm: (i) policy-level dynamic endowment reallocation and (ii) individual-level optimization of cross-game contribution strategies. Extensive experiments demonstrate that our approach achieves 100% full cooperation across diverse hypergraph structures, offering both theoretically grounded insights and actionable pathways for enhancing collective cooperation in complex networked systems.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Humans and AI: Learning Human Values and Preferences

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
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Nearly all living systems, especially humans, depend on collective cooperation for survival and prosperity. However, the mechanisms driving the evolution of cooperative behavior remain poorly understood, particularly in the context of simultaneous interactions involving multiple individuals, repeated encounters, and complex interaction structures. Here, we introduce a novel framework for studying repeated multi-player interactions in structured populations -- repeated multi-player games on hypergraphs -- where multiple individuals within each hyperedge engage in a repeated game, and each player can simultaneously participate in many games. We focus on public goods games, where individuals differ in their initial endowments, their allocation of endowments across games, and their productivity, which determines the impact of their contributions. Through Nash equilibrium analysis, we reveal the intricate interplay between full cooperation (all individuals contribute their entire endowments, maximizing collective benefits) and key factors such as initial endowments, productivity, contribution strategies, and interaction structure. Notably, while equal endowments are most effective in promoting full cooperation in homogeneous hypergraphs, they can hinder cooperation in heterogeneous hypergraphs, suggesting that equal endowments are not universally optimal. To address this, we propose two optimization strategies: one for policymakers to adjust endowment distributions and another for players to modify their contribution strategies. Both approaches successfully promote full cooperation across all studied hypergraphs. Our findings provide novel insights into the emergence of full cooperation, offering valuable guidance for both players and policymakers in fostering collective cooperation.

Problem

• Understanding cooperation evolution in multi-player repeated games
• Analyzing full cooperation's link to endowments, productivity, and structure
• Developing strategies to optimize cooperation in diverse hypergraphs

Innovation

• Repeated multi-player games on hypergraphs
• Nash equilibrium analysis for cooperation
• Optimization strategies for endowment distributions