New game approximates mean curvature flow evolution.
problem Approximating geometric mean curvature flow evolution.
method Two-player zero-sum game with probabilistic elements.
result Value function approximates mean curvature flow.
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48 results for “two-player games”
New algorithm finds near-optimal policies efficiently in zero-sum games.
problem Lack of provable efficiency guarantees for policy optimization in zero-sum games.
method Policy optimization algorithm with function approximation.
result Proves efficient convergence to near-optimal policies with polynomial samples and iterations.
New assumptions and algorithm solve offline two-player zero-sum Markov games.
problem Solving offline two-player zero-sum Markov games under insufficient assumptions.
method Proposed unilateral concentration assumption and pessimism-type algorithm.
result Algorithm efficiently learns Nash equilibrium under unilateral concentration.
Gradient methods converge exponentially in concave network games.
problem Finding Nash equilibria in concave network zero-sum games.
method Gradient Ascent and Optimistic Gradient Ascent analyses.
result Exponential convergence rates in various game settings.
Study proposes new OPE estimators for two-player zero-sum games.
problem Evaluating new policies using historical data from a different policy in multi-player zero-sum games.
method Doubly robust and double reinforcement learning estimators to project exploitability.
result Prove exploitability estimation error bounds and regret bounds for policy profiles.
We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of the state. In this work, we compute the solution of the two-player zero-sum game…
The Linking-Unlinking Gamemath.GT
Combinatorial two-player games have recently been applied to knot theory. Examples of this include the Knotting-Unknotting Game and the Region Unknotting Game, both of which are played on knot shadows. These are turn-based games played by two players, where each player has a separate goal to achieve in order to win the…
Implicit regularisation in stochastic gradient descent: from single-objective to two-player gamesstat.ML
Novel approach finds implicit regularisation in two-player games using BEA.
problem Understanding implicit regularisation in two-player games.
method Using backward error analysis to construct continuous-time flows with gradient-eligible vector fields.
result Identifies new implicit regularisation effects in two-player games.
Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.
problem Gradient-based methods for two-player games suffer from drift due to discrete update steps.
method Derived modified continuous dynamical systems to closely follow the discrete dynamics of games.
result Identified distinct components of discretization drift that can alter or destabilize game performance.
The paper explores how regularization can lead to convergence in imperfect information games.
problem Finding equilibrium in imperfect information games with imperfect information.
method Investigates Follow the Regularized Leader dynamics and how adding a regularization term can lead to strong convergence guarantees.
result The approach leads to algorithms that converge exactly to the Nash equilibrium in imperfect information games.
Optimal algorithm for two-player zero-sum games with linear parameterization.
problem Finding Nash Equilibrium in two-player zero-sum Markov games with linear transition.
method Nash-UCRL algorithm, Coarse Correlated Equilibrium, Optimism-in-Face-of-Uncertainty.
result Proves regret bound, matching lower bound up to logarithmic factors.
Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm is shown to find an -optimal strategy using sample size linear to the number …
Model-Free Learning for Two-Player Zero-Sum Partially Observable Markov Games with Perfect Recallstat.ML
Algorithm learns NE in imperfect information games with imperfect feedback.
problem Learning Nash equilibrium in imperfect information games with bandit feedback.
method IXOMD algorithm for model-free learning with convergence rate.
result IXOMD achieves convergence rate to NE.
In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximiza…
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor we provide an algorithm that computes an -optimal strategy with high-probability given $\tilde{O}((1 - γ)^{-3}…
Optimistic Hedge achieves optimal regret bounds in two-player zero-sum games.
problem Achieving optimal regret bounds for optimistic Hedge in two-player zero-sum games.
method Refined regret analysis and optimization problem formulation.
result Optimistic Hedge achieves regret bounds, matching upper and lower bounds.
Recent work in reinforcement learning demonstrated that learning solely through self-play is not only possible, but could also result in novel strategies that humans never would have thought of. However, optimization methods cast as a game between two players require careful tuning to prevent suboptimal results. Hence,…
A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each player is designed based on Riemann-Finsler geometry. Our approach incorporates a closed loop optimal control and the presentation is familiar wi…
Study Nash equilibrium in non-zero-sum game with Bermudan strategies.
problem Optimizing pay-offs in non-linear non-zero-sum games.
method Recursive construction to find Nash equilibrium.
result Existence of Nash equilibrium in non-zero-sum game.
Paper solves learning imperfect-information games with fewer episodes.
problem Learning imperfect-information extensive-form games from bandit feedback.
method Balanced Online Mirror Descent and Balanced Counterfactual Regret Minimization algorithms.
result Achieves near-optimal sample complexity for finding approximate Nash equilibria.
Paper tackles multiplayer symmetric games, securing equal share for n players.
problem Multiplayer games lack unique equilibria, making guarantees unreliable.
method Identifies conditions for equal share, designs efficient algorithms inspired by no-regret learning.
result Proves algorithms achieve approximate equal share across various settings.
We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank, Soner, Voß (2017). Specifically, both agents track their own stochastic running trading targets while interacting through common aggregated temporary and permanent price impact à la Almgren and Chriss (2001…
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.
Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa, producing highly informative training data on the fly. However, the self-play t…
We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…
The paper analyzes a game where players must balance short-term and long-term interests, leading to cooperative or competitive outcomes.
problem Analyzing time inconsistency in inter-personal decision-making under non-exponential discounting.
method Iterative procedures and Zorn's lemma to find Nash equilibria between players' intra-personal equilibria.
result Inter-personal equilibria exist and depend on the impatience levels of the players.
Game theory applied to splitting surfaces of compact 2-manifolds.
problem Determining the winner in a game played on surfaces of compact 2-manifolds.
method Analyzing the game through Nim addition and series of -values based on increasing genus.
result The -series determines the winner in the game played on compact 2-manifolds.
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the opponent (stochastic, adversarial, or intermediate), the order of the players' mo…
In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market …
We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. W…
This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The pa…
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.
DREAM learns optimal strategies in imperfect games without needing a simulator.
problem Learning optimal strategies in imperfect-information games with multiple agents.
method DREAM is a deep reinforcement learning algorithm that converges to Nash Equilibria and coarse correlated equilibria.
result DREAM achieves state-of-the-art performance in benchmark games and is competitive with simulator-based algorithms.
We study optimal behavior of energy producers under a CO_2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic aspect is captured through a reduced-form price-impact model for the CO_2 allowance…
Optimal strategies are found for a repeated betting game using diffusion approximation.
problem Finding optimal strategies for a repeated betting game with i.i.d. outcomes.
method Constructing a diffusion approximation of the repeated game and analyzing the wealth share process.
result Necessary and sufficient conditions for the wealth share process to be transient or recurrent are derived.
Paper defines a new dimension to measure self-directed learning complexity.
problem Understanding self-directed learning complexity in online learning theory.
method Developed a dimension to characterize self-directed learning mistake-bound.
result Calculated for various concept classes and demonstrated learnability gaps.
This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion . Then we characterize the existence of a Nash equilibrium…
Research tackles alliance formation in many-player zero-sum games, showing reinforcement learning fails but a contract mechanism can help.
problem Tackles the challenge of alliance formation in many-player zero-sum games.
method Demonstrates the social dilemma aspect of alliance formation, introduces a contract mechanism to augment reinforcement learning.
result Naïve reinforcement learning fails to form alliances, but a contract mechanism can help.
Mind the Gap in the Mining Gameq-fin.GN
Game-theoretic analysis of mining gaps in blockchain systems.
problem Strategic mining behavior and its impact on blockchain stability.
method Game-theoretic model and Nash equilibrium analysis.
result Mining gaps can destabilize blockchain systems, especially with decreasing block rewards.
Neural operators approximate Stackelberg game solutions.
problem Intractability of follower's best-response operator in dynamic Stackelberg games.
method Used attention-based neural operators to approximate the best-response operator.
result Approximate best-response operator yields close game value.
Improved model-based reinforcement learning for multi-agent Markov games.
problem Suboptimal sample complexity for model-based algorithms in multi-agent reinforcement learning.
method Optimistic Nash Value Iteration (Nash-VI) for two-player zero-sum Markov games.
result First model-based algorithm matching information-theoretic lower bound with improved sample complexity.
Transformers as Game Players: Provable In-context Game-playing Capabilities of Pre-trained Modelsstat.ML
Transformers learn to play games in-context, proving Nash equilibrium.
problem Understanding in-context game-playing capabilities of pre-trained transformers.
method Theoretical guarantees and constructional results for transformer architecture in multi-agent games.
result Pre-trained transformers can learn Nash equilibrium in-context for two-player zero-sum games.
New algorithm improves sample efficiency for zero-sum Markov games.
problem Improving sample efficiency for model-free algorithms in zero-sum Markov games.
method Proposes a model-free stage-based Q-learning algorithm using variance reduction techniques.
result Achieves optimal sample complexity for finding ε-optimal Nash Equilibrium.
Study learns optimal strategies in imperfect information games with self-play.
problem Learning optimal strategies in imperfect information games.
method Proposes Follow the Regularized Leader (FTRL) algorithms for imperfect information games.
result Proposes two FTRL algorithms: Balanced FTRL and Adaptive FTRL.
The paper explores game-theoretic alignment of LLMs with human preferences, finding limitations and conditions.
problem Aligning LLMs with human preferences using game theory.
method Systematic study of payoff choices in a two-player zero-sum game for desirable alignment properties.
result Impossibility of preference matching in game-theoretic LLM alignment under standard assumptions.
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem is seen as a two-players zero-sum game. An algorithm is proposed to incremental…
We study the problem of multi-agent reinforcement learning (MARL) with adaptivity constraints -- a new problem motivated by real-world applications where deployments of new policies are costly and the number of policy updates must be minimized. For two-player zero-sum Markov Games, we design a (policy) elimination base…
A Policy-Gradient Approach to Solving Imperfect-Information Games with Best-Iterate Convergencecs.GT
Policy gradient method proves convergence in imperfect-information games.
problem Policy gradient methods in imperfect-information games (EFGs).
method Policy gradient approach with best-iterate convergence.
result Policy gradient leads to provable best-iterate convergence in self-play EFGs.