Generative Adversarial Equilibrium Solvers
Denizalp Goktas, David C. Parkes, Ian Gemp, Luke Marris and, Georgios Piliouras, Romuald Elie, Guy Lever, Andrea Tacchetti
TL;DR
This paper presents a novel approach using generative adversarial networks to efficiently approximate equilibria in complex game-theoretic models, including GNE and CE, from limited problem samples.
Contribution
It introduces Generative Adversarial Equilibrium Solvers (GAES), a new neural network framework for learning equilibria in pseudo-games and economic models from samples.
Findings
GAES can learn GNE and CE with high accuracy from limited samples.
The method provides theoretical bounds on computational and sample complexity.
Applications include normal-form games, Arrow-Debreu economies, and environmental economic models.
Abstract
We introduce the use of generative adversarial learning to compute equilibria in general game-theoretic 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,…
Peer Reviews
Decision·ICLR 2024 poster
# Presentation - The paper is well-organized and easy-to-follow: Sec.1 motivates the readers by illustrating the possible applications of GNE solvers, including network communication, cloud computing, and economic models (e.g., Arrow-Debreu exchange economy, Kyoto joint implementation mechanism) # Novelty, Technical Contribution - The formulation of GAES establishes a novel, efficient, simple, and scalable algorithm to train generic GNE solvers. - To the best of my knowledge, most of the pr
# Weaknesses - I don’t see any special weakness in this paper. The authors establish a simple yet powerful framework for training GNE solvers, and backs up their algorithm both with strong theoretical guarantees and empirical results.
1. Introduce a novel method to compute GNE by GAN. 2. Provide theoretical guarantee on convergence and generalization bounds. 3. The performance is better according to the experiments. 4. The literature review in the appendix summarizes the current methods to solve GNE and the application of pseudo games.
1. Assume strong concavity in assumption 1, however, the utility function is not strong convex in Arrow-Debreu competitive economy. 2. Do not provide guarantee for the performance on the training set. 3. Use different network architecture in two experiments which means GAES is not a general solver for GNE.
Pseudo-games are very general game-theoretic models with a number of applications, most notably Arrow-Debreu competitive economies. Yet, there is a lack of scalable techniques for computing generalized Nash equilibria in such settings. This paper makes a concrete contribution in that direction by providing a method with promising performance across a number of benchmarks. The proposed method is natural and the experimental results are overall convincing and quite thorough. Indeed, the paper appe
There are some soundness issues that the authors have to address. First, there appears to be a significant gap between the theoretical analysis and the experimental settings. Specifically, it is not clear how a stationary point in the sense of Theorem 4.1 translates to a GNE. If stationary points are not necessarily GNE, the narrative of the paper has to be restructured. In particular, it is often claimed that the method maps pseudo-games to GNE, and it is not clear whether that claim is theoret
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Taxonomy
TopicsSports Analytics and Performance · Experimental Behavioral Economics Studies · Evolutionary Game Theory and Cooperation