Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the "zero sum fallacy" -- the erroneous belief that one trader in a stock market exch…
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48 results for “zero-sum games”
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.
Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.
problem Understanding dynamics of zero-sum games with hidden structure.
method Gradient Descent Ascent applied to hidden zero-sum games with specific convex-concave structure.
result Gradient Descent Ascent converges to von-Neumann solution in strictly convex-concave hidden games.
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.
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.
Paper studies competitive networks where teams aim to minimize their own objectives, adapting to each other's strategies.
problem Competitive networks where teams have conflicting objectives.
method Proposes diffusion learning algorithms for two classes of network games: zero-sum and non-zero-sum.
result Stability performance of proposed algorithms analyzed and demonstrated through experiments.
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.
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.
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.
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 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…
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…
Large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum gamesstat.ML
This work finds mixed equilibria in zero-sum games using interacting particle dynamics.
problem Finding mixed equilibrium points in continuous minmax games.
method A method based on entropic regularisation of two-layer zero-sum games with interacting particle dynamics.
result The sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity, implying convergence of the empirical measure and the Nikaidô-Isoda error.
Algorithm learns from changing zero-sum games with no regret.
problem Learning in time-varying zero-sum games.
method Developed a single parameter-free algorithm with three performance measures.
result Algorithm recovers best known results for fixed games and adapts to non-stationarity.
Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.
problem Learning dynamics in zero-sum polymatrix games under different information settings.
method Two-timescale learning dynamics combining smoothed best-response updates and TD-learning for estimating local payoff functions.
result Polynomial-time finite-sample guarantees for convergence to an ε-Nash equilibrium in the minimal information case.
Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.
problem Finding mixed Nash equilibria in zero-sum games with multiple players.
method Mean-field gradient descent dynamics with time-averaging, incorporating exponentially discounted gradients.
result Exponential convergence rate to mixed Nash equilibrium with respect to total variation metric.
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can ex…
Paper studies constrained control games with a novel approximation method.
problem Games with constrained control directions.
method Approximation procedure based on -stability estimates and almost sure convergence.
result Existence of game's value and optimal strategy for the stopper.
Mutation improves FTRL convergence in zero-sum games.
problem Lack of last-iterate convergence in FTRL variants.
method Introduced mutation to perturb action probabilities in FTRL.
result M-FTRL converges to Nash equilibria under full-information feedback.
Proposes a new training algorithm for zero-sum games to avoid convergence issues.
problem Gradient-based training leads to weak convergence and cyclic dynamics in zero-sum architectures.
method Follow the perturbed leader algorithm with neural mediating agent.
result Guarantees convergence to mixed Nash equilibrium without cyclic behaviors.
A RL approach finds Nash equilibrium for turn-based zero-sum games.
problem Finding Nash equilibrium in two-player turn-based zero-sum games.
method EIS method combining exploration, policy improvement, and supervised learning.
result EIS method finds an ε-approximate value function of Nash equilibrium in O(ε^(-(d+4))) steps.
The paper solves investment problems with uncertain factors using game theory.
problem Optimal forward investment in an incomplete market with model uncertainty.
method Combining stochastic differential games and ergodic BSDE approach.
result Representation of robust forward performance processes in factor form.
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.
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.
We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…
Paper studies zero-sum games with noisy observations and identifies equilibrium conditions.
problem Zero-sum games with noisy observations of the leader's actions.
method Analyzes the equilibrium of games with noisy action observability, identifies necessary conditions for uniqueness, and investigates the cardinality of best responses.
result The noisy observations significantly impact the cardinality of the follower's set of best responses, and under certain conditions, this set becomes a singleton almost surely.
Paper develops efficient algorithms for zero-sum Markov games with general function classes.
problem Challenging settings in zero-sum Markov games with parameterized value functions or models.
method Developed new model-free and model-based algorithms for decoupled and coordinated settings.
result Improved sample complexity and regret bounds for various settings.
Study of zero-sum games with noisy observations and commitments.
problem Analyzing zero-sum games with noisy observations and commitments.
method Modeling a zero-sum game with a leader committing to a strategy and a follower observing a noisy version of the leader's action.
result Observing the leader's action is either beneficial or immaterial for the follower, and the equilibrium payoff is bounded.
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 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.
New algorithms converge faster to Nash equilibrium in zero-sum games with bandit feedback.
problem Learning in zero-sum games with bandit feedback without communication.
method Developed two uncoupled algorithms achieving optimal rate of .
result Achieved optimal rate of for convergence of policy profiles to Nash equilibrium.
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.
We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.
Paper solves complex game theory problems with new equations.
problem Zero-sum stochastic games with non-Markovian switching.
method New multidimensional SRE and BSDE solutions.
result Existence and uniqueness of SRE solutions.
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…
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.
Pessimistic model-based algorithm finds Nash equilibria in zero-sum Markov games from offline data.
problem Learning Nash equilibria in two-player zero-sum Markov games from limited data.
method Pessimistic model-based algorithm with Bernstein-style lower confidence bounds (VI-LCB-Game).
result Proves sample complexity no larger than , achieving minimax optimality.
Paper analyzes robust strategies in a pension plan game with ambiguous financial markets.
problem Analyzing robust strategies in a defined benefit pension plan game with ambiguous financial markets.
method Formulated and solved two robust non-zero-sum games using stochastic dynamic programming.
result Explicit forms and optimality of the solutions are shown for the firm and union.
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.
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.
We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum game is core to many problems in statistics, optimization, and economics, and fo…
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.
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…
Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a grand challenge. As a first step, we restrict to bilinear zero-sum games and giv…
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…
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.