Multiplayer Cost Games with Simple Nash Equilibria

TL;DR

This paper proves that in multiplayer non zero-sum games with selfish agents, there exist simple Nash equilibria composed of memoryless strategies, which are practical for real-world implementation due to their limited complexity.

Contribution

The paper introduces a class of multiplayer games where simple, memoryless Nash equilibria exist, including for mean-payoff, discounted-payoff, and reachability objectives.

Findings

Existence of Nash equilibria with k memoryless strategies in k-agent games.

Main strategies assume compliance, minor strategies respond to deviations.

Strategies are simple enough for practical implementation.

Abstract

Multiplayer games with selfish agents naturally occur in the design of distributed and embedded systems. As the goals of selfish agents are usually neither equivalent nor antagonistic to each other, such games are non zero-sum games. We study such games and show that a large class of these games, including games where the individual objectives are mean- or discounted-payoff, or quantitative reachability, and show that they do not only have a solution, but a simple solution. We establish the existence of Nash equilibria that are composed of k memoryless strategies for each agent in a setting with k agents, one main and k-1 minor strategies. The main strategy describes what happens when all agents comply, whereas the minor strategies ensure that all other agents immediately start to co-operate against the agent who first deviates from the plan. This simplicity is important, as rational agents are an idealisation. Realistically, agents have to decide on their moves with very limited resources, and complicated strategies that require exponential--or even non-elementary--implementations cannot realistically be implemented. The existence of simple strategies that we prove in this paper therefore holds a promise of implementability.