
In multiagent systems, the complex interaction of fixed incentives can lead agents to outcomes that are poor (\emph{inefficient}) not only for the group, but also for each individual. Price of anarchy is a technical, game-theoretic definition that quantifies the inefficiency arising in these scenarios\textemdash it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable, upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator, agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents do so by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable, D3C resembles the celebrated Win-Stay, Lose-Shift strategy from behavioral game theory, thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting, as is common in multiagent reinforcement learning, we show the upper bound can be reduced via evolutionary strategies, until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox, a prisoner’s dilemma, and several multiagent domains.

Reducing the Price of Anarchy in Multi-Agent Learning


Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we propose an approach that iteratively improves an approximation to a Nash equilibrium through joint play. It accomplishes this by tracing a previously established homotopy that defines a continuum of equilibria for the game regularized with decaying levels of entropy. This continuum asymptotically approaches the \emph{limiting logit equilibrium}, proven by McKelvey and Palfrey (1995) to be unique in \emph{almost} all games, thereby partially circumventing the well-known equilibrium selection problem of many-player games. To encourage iterates to remain near this path, we efficiently minimize \emph{average deviation incentive} via stochastic gradient descent, intelligently sampling entries in the payoff tensor as needed. Monte Carlo estimates of the stochastic gradient from joint play are biased due to the appearance of a nonlinear max operator in the objective, so we introduce additional innovations to the algorithm to alleviate gradient bias. The descent process can also be viewed as repeatedly constructing and reacting to a polymatrix approximation to the game. In these ways, our proposed approach, \emph{average deviation incentive descent with adaptive sampling} (ADIDAS), is most similar to three classical approaches, namely homotopy-type, Lyapunov, and iterative polymatrix solvers. The lack of local convergence guarantees for biased gradient descent prevents guaranteed convergence to Nash, however, we demonstrate through extensive experiments the ability of this approach to approximate a unique Nash equilibrium in normal-form games with as many as seven players and twenty one actions (several billion outcomes) that are orders of magnitude larger than those possible with prior algorithms.

Sample-based Approximation of Nash in Large Many-Player Games via Gradient Descent


**Session Chair:** <br><br> Jivko Sinapov

Oral Session 2A3-1

technical paper

AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

The AAMAS conference series was initiated in 2002 in Bologna, Italy as a joint event comprising the 6th International Conference on Autonomous Agents (AA), the 5th International Conference on Multiagent Systems (ICMAS), and the 9th International Workshop on Agent Theories, Architectures, and Languages (ATAL).

Subsequent AAMAS conferences have been held in Melbourne, Australia (July 2003), New York City, NY, USA (July 2004), Utrecht, The Netherlands (July 2005), Hakodate, Japan (May 2006), Honolulu, Hawaii, USA (May 2007), Estoril, Portugal (May 2008), Budapest, Hungary (May 2009), Toronto, Canada (May 2010), Taipei, Taiwan (May 2011), Valencia, Spain (June 2012), Minnesota, USA (May 2013), Paris, France (May 2014), Istanbul, Turkey (May 2015), Singapore (May 2016), São Paulo (2017) and Stockholm, Sweden (2018), Montreal (May 2019), Auckland (May 2020, Virtual), London (May 2021, Virtual).
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AAMAS 2022

AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

Ian Gemp

2

4

SHORT BIO

Presentations

Reducing the Price of Anarchy in Multi-Agent Learning

Sample-based Approximation of Nash in Large Many-Player Games via Gradient Descent

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