Reach together: How populations win repeated games

2025-10-03

AI Summary

This paper investigates the existence of uniform winning strategies for population players with reachability objectives in parameterized repeated games: given a population of arbitrary size, does there exist a size-independent cooperative strategy guaranteeing victory? Innovatively, we introduce a finite semigroup–based abstraction that reduces strategy existence to the existence of specific elements within the semigroup, thereby uncovering its algebraic essence. By constructing an appropriate semigroup model and integrating formal verification with complexity-theoretic analysis, we prove that the problem is solvable in PSPACE and establish its PSPACE-completeness—marking the first precise characterization of computational complexity for strategy synthesis in such parameterized games.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective. The problem is whether there exists a uniform coalition strategy for the players so that they are sure to win independently of the population size. We use algebraic tools to show that the problem can be solved in polynomial space. First we exhibit a finite semigroup whose elements summarize strategies over a finite interval of population sizes. Then, we characterize the existence of winning strategies by the existence of particular elements in this semigroup. Finally, we provide a matching complexity lower bound, to conclude that repeated population games with reachability objectives are PSPACE-complete.

Problem

• Analyzing coalition strategies for repeated population games
• Determining PSPACE-completeness of reachability objectives
• Developing algebraic methods for strategy summarization

Innovation

• Algebraic tools analyze repeated population games
• Finite semigroup summarizes strategies across populations
• Proves PSPACE-completeness for reachability objectives