Learning equilibria in symmetric auction games using artificial neural networks

Bichler, Martin; Fichtl, Maximilian; Heidekrüger, Stefan; Kohring, Nils; Sutterer, Paul

doi:10.1038/s42256-021-00365-4

Cited by 19 publications

(7 citation statements)

References 29 publications

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“…These are weaker than global equilibria, but the much weaker assumptions guarantee that this result holds for many auctions of interest to economists. In August 2021, the first Journal article relating to my thesis was published in Nature Machine Intelligence (Bichler et al 2021), containing this convergence result and an exhaustive empirical analysis of NPGA, including equilibrium computation in the largest auction (6 bidders, 8 items) where this has been achieved. For further scaling, many challenges remain, e.g.…”

Section: Third Year and Current Statusmentioning

confidence: 98%

Equilibrium Learning in Auction Markets

Heidekrüger

2022

AAAI

Self Cite

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My dissertation investigates the computation of Bayes-Nash equilibria in auctions via multiagent learning. A particular focus lies on the game-theoretic analysis of learned gradient dynamics in such markets. This requires overcoming several technical challenges like non-differentiable utility functions and infinite-dimensional strategy spaces. Positive results may open the door for wide-ranging applications in Market Design and the economic sciences.

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Section: Third Year and Current Statusmentioning

confidence: 98%

Equilibrium Learning in Auction Markets

Heidekrüger

2022

AAAI

Self Cite

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“…In regard to finding optimal economic designs, deep learning has been used for problems of auction design (Dütting et al, 2019;Curry et al, 2022c;Tacchetti et al, 2019;Curry et al, 2022a;Gemp et al, 2022;Rahme et al, 2020) and matching (Ravindranath et al, 2021). In regard to solving for equilibria, some recent works have tried to solve for Nash equilibria in auctions (Heidekrüger et al, 2019;Bichler et al, 2021), and dynamic stochastic general equilibrium models (Curry et al, 2022b;Chen et al, 2021;Hill et al, 2021).…”

Section: Additional Related Workmentioning

confidence: 99%

Generative Adversarial Equilibrium Solvers

Denizalp¹,

Parkes²,

Gemp³

et al. 2023

Preprint

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We introduce the use of generative adversarial learning to compute equilibria in general gametheoretic settings, specifically the generalized Nash equilibrium (GNE) in pseudo-games, and its specific instantiation as the competitive equilibrium (CE) in Arrow-Debreu competitive economies. Pseudo-games are a generalization of games in which players' actions affect not only the payoffs of other players but also their feasible action spaces. Although the computation of GNE and CE is intractable in the worst-case, i.e., PPAD-hard, in practice, many applications only require solutions with high accuracy in expectation over a distribution of problem instances. We introduce Generative Adversarial Equilibrium Solvers (GAES): a family of generative adversarial neural networks that can learn GNE and CE from only a sample of problem instances. We provide computational and sample complexity bounds, and apply the framework to finding Nash equilibria in normal-form games, CE in Arrow-Debreu competitive economies, and GNE in an environmental economic model of the Kyoto mechanism.

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“…actually have continuous action spaces. Examples include continuous resource allocation games [Ganzfried, 2021], security games in continuous spaces [Kamra et al, 2017;Kamra et al, 2018;Kamra et al, 2019], network games [Ghosh and Kundu, 2019], simulations of military scenarios and wargaming [Marchesi et al, 2020], and most video games [Berner et al, 2019;Vinyals et al, 2019]. Furthermore, even if the action space is discrete, it may be fine-grained enough to treat as continuous for computational efficiency purposes [Borel, 1938;Chen and Ankenman, 2006;Ganzfried and Sandholm, 2010].…”

Section: Introductionmentioning

confidence: 99%

Finding Mixed-Strategy Equilibria of Continuous-Action Games without Gradients Using Randomized Policy Networks

Martín

Sandholm

2023

Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence

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We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black box. To tackle this problem, we apply zeroth-order optimization techniques that combine smoothed gradient estimators with equilibrium-finding dynamics. We model players' strategies using artificial neural networks. In particular, we use randomized policy networks to model mixed strategies. These take noise in addition to an observation as input and can flexibly represent arbitrary observation-dependent, continuous-action distributions. Being able to model such mixed strategies is crucial for tackling continuous-action games that lack pure-strategy equilibria. We evaluate the performance of our method using an approximation of the Nash convergence metric from game theory, which measures how much players can benefit from unilaterally changing their strategy. We apply our method to continuous Colonel Blotto games, single-item and multi-item auctions, and a visibility game. The experiments show that our method can quickly find a high-quality approximate equilibrium. Furthermore, they show that the dimensionality of the input noise is crucial for performance. To our knowledge, this paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.

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Learning equilibria in symmetric auction games using artificial neural networks

Cited by 19 publications

References 29 publications

Equilibrium Learning in Auction Markets

Equilibrium Learning in Auction Markets

Generative Adversarial Equilibrium Solvers

Finding Mixed-Strategy Equilibria of Continuous-Action Games without Gradients Using Randomized Policy Networks

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