Securing Equal Share: A Principled Approach for Learning Multiplayer Symmetric Games (2406.04201v2)

Abstract: This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games, equilibria in multiplayer games are neither unique nor non-exploitable, failing to provide meaningful guarantees when competing against opponents who play different equilibria or non-equilibrium strategies. This gives rise to a series of long-lasting fundamental questions in multiplayer games regarding suitable objectives, solution concepts, and principled algorithms. This paper takes an initial step towards addressing these challenges by focusing on the natural objective of equal share -- securing an expected payoff of C/n in an n-player symmetric game with a total payoff of C. We rigorously identify the theoretical conditions under which achieving an equal share is tractable and design a series of efficient algorithms, inspired by no-regret learning, that provably attain approximate equal share across various settings. Furthermore, we provide complementary lower bounds that justify the sharpness of our theoretical results. Our experimental results highlight worst-case scenarios where meta-algorithms from prior state-of-the-art systems for multiplayer games fail to secure an equal share, while our algorithm succeeds, demonstrating the effectiveness of our approach.

• The paper introduces novel equilibrium concepts that guarantee non-negative expected payoffs for AI agents in multiplayer symmetric games.
• It develops an algorithmic framework combining behavior cloning with the Hedge and SAOL algorithms to handle both stationary and adaptive opponents.
• Empirical results reveal that the proposed method reliably outperforms traditional self-play approaches, ensuring equitable outcomes in dynamic environments.

Towards Principled Superhuman AI for Multiplayer Symmetric Games

The paper "Towards Principled Superhuman AI for Multiplayer Symmetric Games" addresses the intricate challenges and open questions that arise in multiplayer symmetric games, diverging significantly from the extensively studied two-player zero-sum games. Multiplayer games, fundamentally different due to the non-uniqueness of equilibria and the associated risk of players performing suboptimally, necessitate new solution concepts and algorithmic frameworks. This paper makes notable contributions by providing a rigorous definition of solution concepts as well as provable algorithms tailored to multiplayer symmetric normal-form games.

Key Contributions

Conceptual Challenges in Multiplayer Games

The research begins by highlighting two critical questions: (1) What is the correct solution concept for AI agents in multiplayer games? and (2) What is the general algorithmic framework that can provably solve all games within this class?

First, the paper discusses the limitations of standard equilibria, demonstrating that classical Nash Equilibria (NE), Correlated Equilibria (CE), and Coarse Correlated Equilibria (CCE) are insufficient to secure a non-negative expected payoff in multiplayer settings. A key insight is the inadequacy of these equilibria due to the non-uniqueness and potential for significant variations in varied gameplay scenarios.

New Solution Concepts

The authors introduce new solution concepts tailored to multiplayer symmetric games. They argue that to reliably secure an "equal share" or non-negative expected payoff, it is paramount that AI agents adapt their strategies to those of their opponents, particularly when all opponents employ identical strategies. This leads to defining new equilibrium notions where AI agents must adapt to the identical strategy adopted by opponents, contrasting sharply with the assumption of diverse opponent strategies in prior works.

Algorithmic Framework

To tackle the dynamic and often adversarial nature of multiplayer games, the authors propose a combination of behavior cloning and no-regret learning algorithms. Their approach leverages the Hedge algorithm, which is then extended to handle stationary and adaptive opponents through no-dynamic-regret learning, achieving compelling theoretical guarantees.

1. Stationary Opponents: The Hedge algorithm, under this setting, is shown to achieve an average payoff, proving its efficiency in games where opponents' strategies remain constant.
2. Adaptive Opponents: Addressing the non-stationary scenarios, they deploy the Strongly Adaptive Online Learner (SAOL) algorithm, which offers robust guarantees despite the variations in opponent strategies. This ensures the agent can still secure an equal share even when opponents evolve their strategies slowly.

Experimental Validation

Through empirical evaluations, the paper confirms the limitations of previous state-of-the-art systems that rely on self-play from scratch. In particular, it is shown that these traditional methods can converge to suboptimal solutions in the face of non-stationary and non-collaborative opponent policies. Conversely, the proposed method, which combines opponent modeling with best response adaptation, consistently outperforms human-like policies and secures a non-negative expected payoff in various game scenarios.

Implications and Future Directions

The implications of this research are manifold, offering both practical and theoretical advancements. Practically, it provides a pathway to devising robust AI agents for a wide array of multiplayer games beyond the traditionally studied ones like Poker and Mahjong. Theoretically, it prompts a re-evaluation of solution concepts in game theory, especially in environments characterized by symmetry and multi-agent interactions.

The paper’s insights into no-regret learning and adaptation open avenues for further developing AI that can thrive in highly dynamic and interactive settings. Future research might extend these results to more complex game structures like extensive-form games, possibly integrating advanced learning techniques such as deep reinforcement learning.

In conclusion, the paper offers a principled approach to developing superhuman AI for multiplayer symmetric games, addressing foundational challenges and proposing novel solutions with strong theoretical backing and practical effectiveness. This work sets the stage for creating more intelligent and adaptive AI agents capable of navigating the complexities of multiplayer interactions.