arXiv research

New findings show pure strategy equilibria are more robust in a war of attrition game.

This work finds mixed equilibria in zero-sum games using interacting particle dynamics.

We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an infinite-dimensional two-player game and prove rigorous convergence rates to the mixed NE, reso…

Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not typically met in practice. Mixed Nash equilibria exist in greater generality and may be …

This work finds mixed equilibria in machine learning problems using measures and simultaneous gradient ascent-descent.

Given a multifunction from $X$ to the $k-$fold symmetric product $Sym_k(X)$, we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…

We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class of variable concession games which generalize wars of attrition. Previously know…

No-regret learning fails to converge to Nash equilibria in mixed strategies.

We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our…

This work models GHG offset credit markets to find optimal strategies for market participants.

Two new RL methods enable deep learning of MFG equilibria.

Investigates market dynamics with informed traders and high-frequency traders.

In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. The presence of ties in the agents' best-response correspondences yields discontinuous payoff functi…

Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.

Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.

Study strategic competition in commodity markets using impulse-switching controls.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that me…

Study shows randomized strategies can't be Nash equilibria in markets with transient price impact.

Modeling gas fee competition in decentralized exchanges to optimize arbitrage profits.

The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.

We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…

For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.

Paper develops efficient algorithms for learning rationalizable equilibria in multiplayer games.

A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …

Study global geometry of dynamical systems with entire vector fields.

New results on financial equilibria in markets with general semimartingales.

We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof is also useful in studying the bifurcation of relative equilibria.

This paper analyzes complex equilibria in a networked bivirus epidemic model.

We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.

Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the equilibrium allocation are m…

In this paper the possibility of computing equilibrium in pure exchange and production economies by a homotopy method is investigated. The performance of the algorithm is tested on examples with known equilibria taken from the literature on general equilibrium models and numerical results are presented. In computing eq…

The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.

Study of MHD equilibria with orientation-reversing symmetry, showing all orbits are periodic.

Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.

New method finds all Nash equilibria via vector optimization.

We obtain a formula for the number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the winding number of the evolute of $\partial K$ with respect to $O$. The formula extends to the case where $O$ lies on the evolute of $\partial K$ and a suitably modified version ho…

We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here we argue in favor of the usefulness of …

Study optimal stopping times for multi-dimensional processes with non-exponential discounting.

We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations and is…

We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.

New approach tackles non-stationary multi-agent games with black-box methods.

Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal constraints.We deal with random endowment density streams which admit jumps and g…

In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We p…

Study explores optimal strategies in games with multiple players and mean-field interactions.

The paper solves portfolio optimization problems with risk constraints.

Generative Adversarial Networks (GAN) have become one of the most successful frameworks for unsupervised generative modeling. As GANs are difficult to train much research has focused on this. However, very little of this research has directly exploited game-theoretic techniques. We introduce Generative Adversarial Netw…

Optimal fees for CFMMs prevent liquidity pools from competing to the bottom.