arXiv research

Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.

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 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…

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

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

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…

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

PAPAL algorithm finds mixed Nash equilibria in continuous games.

New method finds all Nash equilibria via vector optimization.

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

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

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

In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substan…

Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.

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…

The paper solves portfolio optimization problems with risk constraints.

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…

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

Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found…

Algorithm converges to Nash equilibria in competitive games.

Study Nash equilibria in mean field portfolio games with consumption.

The paper analyzes game theory in convertible contracts during liquidity events.

Two firms compete in a financial market, choosing dividend strategies to avoid default and maximize profits.

This research uses reinforcement learning to find optimal emission offsets in greenhouse gas markets.

Modeling reinsurance market, we find subgame perfect Nash equilibria.

We consider a market impact game for $n$ risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a mean-variance functional of their costs or to maximize the expected exponential u…

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…

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…

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial…

We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum linear quadratic games, a classic game setting which is recently emerging as a b…

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…

We study the system of heterogeneous interbank lending and borrowing based on the relative average of log-capitalization given by the linear combination of the average within groups and the ensemble average and describe the evolution of log-capitalization by a system of coupled diffusions. The model incorporates a game…

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

GANs may not have Nash equilibria, but proximal training can find solutions.

Modeling European spot power markets with game theory for Nash equilibria.

Distributed strategic learning has been getting attention in recent years. As systems become distributed finding Nash equilibria in a distributed fashion is becoming more important for various applications. In this paper, we develop a distributed strategic learning framework for seeking Nash equilibria under stochastic…

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…

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

Study on liquidity and market efficiency in auction games with imperfect information.

Deep learning solves complex PA mean field games with market-clearing conditions.

Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning method…

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

We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a $N$-player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error fo…

Study on market instability in multi-agent trading with price impact and transaction costs.

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconve…

Last-iterate guarantees for learning in co-coercive games under noisy feedback.

Study analyzes portfolio liquidation games influenced by self-exciting order flow.