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…
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48 results for “generalized Nash equilibria”
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.
problem Existence and uniqueness of Nash equilibria in multiplicative performance criteria games.
method General characterization of Nash equilibria for a large class of utility functions.
result Existence and uniqueness of Nash equilibria for arbitrary initial wealth vectors.
Study shows randomized strategies can't be Nash equilibria in markets with transient price impact.
problem Existence of pure Nash equilibria in markets with transient price impact.
method Considered randomized strategies and showed that they cannot be Nash equilibria.
result Nash equilibria cannot contain randomized strategies.
The paper proposes a method to learn continuous-action graphical games from perturbed equilibria.
problem Learning the exact structure of continuous-action graphical games from limited data.
method A block regularized method to recover the graphical game structure.
result The method recovers the exact structure of the graphical game under certain conditions.
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…
Policy-gradient algorithms fail to converge to Nash equilibria in continuous state and action space games.
problem Policy-gradient algorithms lack convergence guarantees in multi-agent continuous state and action space games.
method Analysis of gradient-play in linear quadratic games, showing non-convexity and counterexamples.
result Policy-gradient algorithms can avoid Nash equilibria in certain continuous state and action space games.
The paper solves portfolio optimization problems with risk constraints.
problem Maximizing utility while ensuring a certain wealth threshold with risk constraints.
method Derives Nash equilibria for two agents and characterizes them for more than two agents.
result Characterizes Nash equilibria for different cases of competition probabilities.
Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.
problem Finding Nash equilibria in two-player zero-sum continuous games, especially in high dimensions.
method Parametrizing mixed strategies as mixtures of particles, updating their positions and weights using gradient descent-ascent.
result Global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic.
Deep Q-Learning method for Nash equilibria in stochastic games.
problem Model-free learning for multi-agent stochastic games, especially for general-sum games.
method Data-efficient Deep-Q-learning using local linear-quadratic expansion parametrized by deep neural networks.
result The algorithm learns optimal actions for stochastic games without experiencing all state-action pairs.
The paper analyzes strategic behavior in reinsurance transactions leading to Nash equilibria.
problem Strategic behavior in reinsurance transactions affecting risk aversion and welfare gains.
method Identifying Nash equilibria within a class of risk measures.
result At strictly beneficial Nash equilibria, agents appear homogeneous in risk preferences.
Given a multifunction from to the fold symmetric product , 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…
Study Nash equilibria in mean field portfolio games with consumption.
problem Finding Nash equilibria in mean field portfolio games with consumption.
method Established a correspondence between equilibria and solutions to FBSDEs, using martingale and dynamic programming principles.
result Proved the uniqueness of Nash equilibrium in closed form under certain conditions.
Entropy-Norm space for geometric selection of strict Nash equilibria in n-person gamesphysics.soc-ph
Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.
problem Finding a fair Nash equilibrium in group decision-making.
method Introduces entropy-norm space for geometric selection of strict Nash equilibria.
result The closest entropy-norm pair to the largest entropy-norm pair in rescaled space is the most suitable equilibrium.
The paper analyzes game theory in convertible contracts during liquidity events.
problem Optimizing payments in convertible contracts during liquidity events.
method Defined a general model for games, showed non-existence of pure strategy Nash equilibria, developed algorithms for computing equilibria.
result Optimum pure strategy Nash equilibria exist when all contracts are of the same type (SAFE).
Study network equilibria in saturated systems, revealing how small shocks can trigger major losses.
problem Understanding how small shocks can lead to major losses in financial networks and games.
method Derived explicit expressions for network equilibria, proved conditions for their uniqueness, and analyzed discontinuities.
result Bifurcation phenomenon in network equilibria, showing sensitivity to small shocks.
Policy optimization converges to Nash equilibria in zero-sum LQ games.
problem Finding Nash equilibria in zero-sum linear quadratic games.
method Developed three projected nested-gradient methods to converge to NE.
result Policy optimization methods converge to Nash equilibria in zero-sum LQ games.
Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximationcs.LG
Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.
problem Learning Nash equilibria in zero-sum stochastic games is computationally expensive.
method Entropy-regularized soft policies for Q-function updates.
result Algorithm converges to Nash equilibrium under certain conditions.
Modeling reinsurance market, we find subgame perfect Nash equilibria.
problem Optimizing reinsurance market with multiple insurers and reinsurers.
method Sequential game with Subgame Perfect Nash Equilibria analysis.
result Characterized subgame perfect Nash equilibria in some market cases.
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…
Algorithm converges to Nash equilibria in competitive games.
problem Finding Nash equilibria in decentralized, competitive Markov games.
method Decentralized Optimistic Gradient Descent/Ascent with a critic.
result Converges to the set of Nash equilibria under self-play.
This research uses reinforcement learning to find optimal emission offsets in greenhouse gas markets.
problem Finding optimal emission offsets in greenhouse gas markets to control excess emissions.
method Utilized reinforcement learning, specifically Nash-DQN, to estimate market Nash equilibria.
result Emitting firms can achieve significant financial savings by abiding by the Nash equilibria found in the market.
GANs may not have Nash equilibria, but proximal training can find solutions.
problem Existence of Nash equilibria in GANs optimization.
method Proximal training approach to find solutions.
result Proximal training finds solutions to GAN problems.
Two firms compete in a financial market, choosing dividend strategies to avoid default and maximize profits.
problem Strategic interaction between two financially constrained firms in a market with default risk.
method Construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control.
result Explicit identification of optimal strategies and equilibrium payoffs for different initial conditions.
Study interbank lending and borrowing dynamics with heterogeneous mean field model.
problem Modeling systemic risk in a network of banks with varying capitalization.
method Developed a mean field type model with coupled diffusions to describe log-capitalization evolution.
result Existence of Nash equilibria in large-scale heterogeneous interbank networks.
This work models GHG offset credit markets to find optimal strategies for market participants.
problem Optimizing GHG offset credit markets to reduce emissions and penalize excess emissions.
method Characterized optimal behavior in single-player and two-player GHG offset credit markets using optimal stopping and control problems, and mixed-Nash equilibria.
result Market participants benefit from optimal OC trading and generation, highlighting the importance of acting optimally.
The paper analyzes data markets with multiple data aggregators, showing non-uniqueness of equilibria and social inefficiency.
problem Non-uniqueness of equilibria and social inefficiency in data markets with multiple data aggregators.
method Characterization of generalized Nash equilibria and analysis of necessary and sufficient conditions for social inefficiency.
result There are either infinitely many or no generalized Nash equilibria, leading to social inefficiency.
Nash equilibrium for risk-averse investors in a market impact game with transient price impactq-fin.TR
We consider a market impact game for 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…
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…
Study on liquidity and market efficiency in auction games with imperfect information.
problem Generating liquidity in illiquid auction markets with imperfect information.
method Characterized Nash equilibria in a two-player game with imperfect information, linking market spreads to signal strength.
result Without incentives, the market is inefficient and does not lead to trades. Quadratic fees indexed on half spread can generate liquidity.
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 -player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error fo…
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 -player equilibria converges to it as . However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that me…
Optimal fees for CFMMs prevent liquidity pools from competing to the bottom.
problem Maximizing liquidity provider returns in CFMMs with multiple pools.
method Theoretical and numerical analysis of Nash equilibria for optimal fees.
result Pure Nash equilibria of optimal fees exist for CFMMs using Uniswap's trade function.
Modeling European spot power markets with game theory for Nash equilibria.
problem Optimizing electricity markets with risk-averse players and constraints.
method Game-theoretic framework with Jacobi and Gauss-Seidel schemes for approximate Nash equilibria.
result Innovative risk aversion model reduces price dimensionality and ensures boundedness.
Study on hypothesis testing games with adversarial classification, showing convergence rates.
problem Adversarial classification in hypothesis testing.
method Mixed strategy Nash equilibria analysis, concentration phenomena examination.
result Exponential rates of convergence of classification errors at equilibrium.
Last-iterate guarantees for learning in co-coercive games under noisy feedback.
problem Learning in co-coercive games with noisy feedback.
method Vanilla stochastic gradient descent with a new noise model.
result Last-iterate bound of order for co-coercive games.
Study on market instability in multi-agent trading with price impact and transaction costs.
problem Analyzing market instability in multi-agent trading with price impact and transaction costs.
method Analytical and numerical methods to study Nash equilibria and stability conditions.
result Conditions on model parameters determine market stability, including scaling of market impact and transaction cost.
Paper optimizes multi-agent learning in Markov games with generative model.
problem Learning Nash or CCE equilibria in multi-agent Markov games.
method Develops \myalg~algorithm and adaptive sampling scheme using FTRL method.
result Minimax-optimal learning of CCE with minimal samples.
We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical systems theory. For both general-sum and potential games, we characterize a non…
Study analyzes portfolio liquidation games influenced by self-exciting order flow.
problem Analyzing portfolio liquidation strategies with market order dynamics.
method Mean-field control problem, novel FBSDE system, sufficient maximum principle.
result Existence and uniqueness of open-loop Nash equilibria proved.
Study optimal investment in large populations of competitive, heterogeneous agents.
problem Maximizing utility in a large, interacting agent system with relative performance concerns.
method Analyzes stochastic utility maximization game in finite and infinite agent settings, using graphon models and backward stochastic differential equations.
result Convergence of Nash equilibria and optimal utilities from finite to infinite agent models under specific conditions.
Deep learning solves complex PA mean field games with market-clearing conditions.
problem Optimizing Principal-Agent interactions in renewable energy markets with market-clearing conditions.
method Actor-critic approach, deep backward stochastic differential equations (BSDE), neural net approximation.
result Efficacy of the deep learning algorithm in solving complex PA mean field games.
Model shows how advisors can manipulate naive investors.
problem How financial advisors manipulate naive investors.
method Agent-Based Model with Nash equilibria and best response functions.
result Greediness/naivety of investors emerge naturally from the model.
Generative adversarial networks (GANs) evolved into one of the most successful unsupervised techniques for generating realistic images. Even though it has recently been shown that GAN training converges, GAN models often end up in local Nash equilibria that are associated with mode collapse or otherwise fail to model t…
Study strategic competition in commodity markets using impulse-switching controls.
problem Strategic competition between upstream and downstream firms in commodity markets.
method Non-zero-sum stochastic differential game with mixed impulse/switching controls.
result Multiple Nash equilibria found, depending on the number of switches by the downstream firm.
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our appr…
Investigates portfolio selection among competitive agents with mean-variance preferences.
problem Optimizing portfolios with multi-agent competition and relative wealth comparison.
method Reformulated as a constrained, non-homogeneous stochastic linear-quadratic control problem; derived optimal feedback strategies; used decoupling techniques and fixed-point theory to solve nonlinear BSDEs.
result Characterized three scenarios based on market and competition parameters: unique Nash equilibrium, no Nash equilibrium, or infinitely many Nash equilibria.
Learning Two-Player Mixture Markov Games: Kernel Function Approximation and Correlated Equilibriumcs.LG
Algorithm finds Nash equilibria in complex games with function approximation.
problem Learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation.
method Online learning algorithm using upper and lower confidence bounds derived from optimism in the face of uncertainty.
result Achieves regret with polynomial complexity, under mild assumptions.