Anna Jaśkiewicz, Andrzej S. Nowak
In this paper, we consider constrained discounted stochastic games with a countably generated state space and norm continuous transition probability having a density function. We prove existence of approximate stationary equilibria and stationary weak correlated equilibria. Our results imply the existence of stationary Nash equilibrium in $ARAT$ stochastic games.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Multiple-Population Discrete-Time Mean Field Games with Discounted and Total Payoffs: The Existence of Equilibria
本文提出了多群体离散时间平均场博弈模型，在一般假设下首次证明了平稳和Markov平均场均衡的存在性，涵盖折扣与总收益准则，并扩展了单群体理论。
The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independent transitions, and stochastic games with mixtures of constant transition kernels as special cases. A remarkably simple proof is provided via establishing a new connection between stochastic games and conditional expectations of correspondences. New applications of stochastic gam…
Stationary Discounted and Ergodic Mean Field Games of Singular Control
本文研究奇异控制下的平稳平均场博弈，证明贴现与遍历两种准则下均衡的存在唯一性，并通过阿贝尔极限建立二者联系，从而用贴现博弈的平均场均衡近似对称N人遍历博弈的纳什均衡。
Characterization and Computation of Feedback Nash Equilibria in Scalar Discounted N-Player Linear Quadratic Games
研究标量折扣线性二次博弈中反馈纳什均衡，区分稳定与非稳定均衡，提出参数化表征和数值计算方法，并导出对称博弈的闭式解及多重均衡条件。
We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a discounted payoff are satisfied. We are interested in the existence of a Nash or noncooperative equilibrium. Under suitable conditions, which include absolute continuity of the transitions with respect to some reference probability measure, additivity of the payoffs and the transition probabilities (ARAT condition), and continuity in action of the payoff func…
On Two-Player Scalar Discounted Linear Quadratic Games
本文研究了线性二次博弈中反馈纳什均衡的特性，通过分析离散时间折扣耦合最佳响应方程和局部鞍点分类工具，揭示了多重解情况下反协调方案的重要性，并给出了对称情况下的闭式解和均衡存在性条件。
On the Nash Equilibria of a Simple Discounted Duel
本文将双人静态决斗建模为非零和折扣随机博弈，证明除了始终射击策略外，该博弈在平稳与非平稳策略下均存在合作性（不射击）纳什均衡，并探讨了其与重复囚徒困境的相似性。
Markov-Nash Equilibria in Mean-Field Games with Discounted Cost
本文研究了具有有限数量智能体的离散时间均场博弈，考虑了无限 horizon 折扣成本优化准则，引入了马尔可夫-纳什均衡概念，证明了在智能体数量趋于无穷时均场均衡的存在性，并展示了在足够多智能体时该均衡策略近似为马尔可夫-纳什均衡。
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an infinite horizon discounted individual cost, we show existence of a stationary equilibrium, and prove its uniqueness under a positive externality condition. We further analyze comparative statics of the stationary equilibrium by quantitatively determining the impact of the effort cost.
Synchronization Games
本研究提出双状态平均场博弈模型研究同步现象，刻画了稳态与动态均衡及稳定性，揭示了相互作用强度变化引发的相变规律，以及不同成本设定下的均衡演化特征。
Independent Reinforcement Learning in Discounted Markov Games
针对折扣一般和马尔可夫博弈，在假设ETH与PPAD等价下证明独立学习无多项式时间算法，提出首个完全解耦的分层乐观镜像下降算法，保证次指数收敛并开发全反馈与部分反馈版本。
We consider stochastic differential games with $N$ nearly identical players, linear-Gaussian dynamics, and infinite horizon discounted quadratic cost. Admissible controls are feedbacks for which the system is ergodic. We first study the existence of affine Nash equilibria by means of an associated system of $N$ Hamilton-Jacobi-Bellman and $N$ Kolmogorov-Fokker-Planck partial differential equations, proving that for small discount factors quadratic-Gaussian solutions exist and are unique. Then, we prove the convergence of such solutions to the unique quadratic-Gaussian solution of the pair of M…
Nash equilibria for total expected reward absorbing Markov games: the constrained and unconstrained cases
本文研究抽象可测状态空间上非零和N人吸收马尔可夫博弈，在总期望收益准则下，证明约束与无约束问题中马尔可夫策略构成非合作均衡，并推出折扣模型的纳什均衡存在性。
We construct an approximate public-signal correlated equilibrium for a nonzero-sum differential game in the class of stochastic strategies with memory. The construction is based on a solution of an auxiliary nonzero-sum continuous-time stochastic game. This class of games includes stochastic differential games and continuous-time Markov games. Moreover, we study the limit of approximate equilibrium outcomes in the case when the auxiliary stochastic games tend to the original deterministic one. We show that it lies in the convex hull of the set of equilibrium values provided by deterministic pu…
Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games
该研究针对带折扣和熵正则化的非平稳连续时间平均场博弈，证明大折扣率下有限时域MFG满足与时域无关的收缩条件，推导了有限与无限时域均衡的收敛率及相关误差界。
In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of solution is justified in two ways: We prove that correlated solutions arise as limits of exchangeable correlated equilibria in restricted (Markov open-loop) strategies for the underlying $N$-player games, and we show how to construct approximate $N$-player correlated equilibria starting from a correlated solution to the mean field game.
In a discrete space and time framework, we study the mean field game limit for a class of symmetric $N$-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows to construct approximate $N$-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.
Robustness and Approximation of Discrete-time Mean-field Games under Discounted Cost Criterion
本文研究了在模型不确定性下离散时间均场均衡的鲁棒性，通过价值迭代算法的收敛条件，证明了系统动态误标情况下均场均衡的鲁棒性，并展示状态空间量化足够精细时有限模型的均场均衡近似于名义解。
Our paper concerns the computation of Nash equilibria of first-price auctions with correlated values. While there exist several equilibrium computation methods for auctions with independent values, the correlation of the bidders' values introduces significant complications that render existing methods unsatisfactory in practice. Our contribution is a step towards filling this gap: inspired by the seminal fictitious play process of Brown and Robinson, we present a learning heuristic-that we call fictitious bidding (FB)-for estimating Bayes-Nash equilibria of first-price auctions with correlated…
We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator, whose fixed point is a mean-field equilibrium (i.e. equilibrium in the infinite population limit). We first prove that this operator is a contraction, and propose a learning algorithm to compute an approximate mean-field equilibrium by approximating the MFE operator with a random one. Moreover, using the contraction property of the MFE operator, we establish t…
This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case of two departments are given. Utilitarian, egalitarian, republican and libertarian concepts of correlated equi…
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria: discounted and ergodic. Under the Lasry--Lions monotonicity condition we characterize the stationary ergodic mean field game equilibrium by a mean field game system of two coupled equations: one for the value and the other for the stationary measure. This system is linked with the ergodic master equation. Several discounted mean field game systems are utili…
Decentralized Bandit Learning of Markov Perfect Equilibria
针对具有连续动作的一般和马尔可夫博弈，提出分散式多臂老虎机学习方法，基于同时扰动随机近似更新动作，证明其几乎必然收敛到唯一平稳马尔可夫完美均衡，收敛速率为$O(n^{-1/2})$，并扩展至情节有限时域学习。
Coarse correlated equilibria for continuous time mean field games in open loop strategies
本文在连续时间对称随机微分博弈中引入平均场博弈的粗糙相关解，通过极小极大定理证明其存在性，并证明其能诱导 $N$ 人博弈的近似粗糙相关均衡。
A Coupled Optimization Framework for Correlated Equilibria in Normal-Form Game
本文提出非正则化博弈框架，将正则形式博弈的策略提升为联合行动上的非正则化测度，并通过熵正则化获得具有闭式解的次优相关均衡，为相关均衡建立了耦合优化基础。
Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning
针对连续时间平均场博弈，提出最优粗相关均衡的线性规划刻画，并设计基于拉格朗日对偶的无遗憾学习算法，给出收敛速率。
Approximation of Discrete-Time Infinite-Horizon Mean-Field Equilibria via Finite-Horizon Mean-Field Equilibria
该研究严格证明有限时域平均场博弈的均衡聚点可逼近无限时域的非平稳与平稳均衡，改进了迭代收缩率，推导了指数衰减误差界并提出新的唯一性判据，还可支撑未知系统下的学习逼近方法。
We investigate the consequences of allowing players to adopt strategies which take advantage of quantum randomization devices. In games of full information, the resulting equilibria are always correlated equilibria, but not all correlated equilibria appear as quantum equilibria. The classical and quantum theories diverge further in games of private information. In the quantum context, we show that Kuhn's equivalence between behavioral and mixed strategies breaks down. As a result, quantum technology allows players to achieve outcomes that would not be achievable with any classical technology s…
The dual reduction process, introduced by Myerson, allows to reduce a finite game into a smaller dimensional game such that any equilibrium of the reduced game is an equilibrium of the original game. This holds both for Nash equilibrium and correlated equilibrium. We present examples of applications of dual reduction and argue that this is a useful tool to study Nash equilibria and correlated equilibria. We then investigate its properties.
In the literature, existence of mean-field equilibria has been established for discrete-time mean field games under both the discounted cost and the average cost optimality criteria. In this paper, we provide a value iteration algorithm to compute mean-field equilibrium for both the discounted cost and the average cost criteria, whose existence proved previously. We establish that the value iteration algorithm converges to the fixed point of a mean-field equilibrium operator. Then, using this fixed point, we construct a mean-field equilibrium. In our value iteration algorithm, we use $Q$-funct…
This document consists of two parts: the second part was submitted earlier as a new proof of Nash's theorem, and the first part is a note explaining a problem found in that proof. We are indebted to Sergiu Hart and Eran Shmaya for their careful study which led to their simultaneous discovery of this error. So far the error has not been fixed, but many of the results and techniques of the paper remain valid, so we will continue to make it available online. Abstract for the original paper: We give a novel proof of the existence of Nash equilibria in all finite games without using fixed point the…
Coarse correlated equilibria in linear quadratic mean field games and application to an emission abatement game
该研究在线性二次平均场博弈框架下提出计算平均场粗相关均衡（CCE）的方法，在减排博弈中验证发现这类CCE能显著优于平均场纳什均衡，拉近其与社会最优解的差距。
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same type of constraints as in [1], i.e., player 1 has subscription based constraints and player 2, who controls the transition probabilities, has realization based constraints which can also depend on the strategies of player 1. Next, we consider a N -player nonzero sum constrained stochastic game with independent state processes where each player has average cost …
Convergence of Potential Mean-Field Games via Lyapunov Methods
本文研究了无折扣无限时间潜在均场博弈的收敛性，通过Lyapunov函数证明了时间趋于无穷时弱极限点为 stationary equilibria，且在 stationary 解唯一时均衡收敛，并给出了新的唯一性准则。
Computational analysis on a linkage between generalized logit dynamic and discounted mean field game
本研究基于折扣 mean field game 为广义 logit 动态提供了新解释，论证大折扣极限产生 logit 动态，讨论了适定性，并提出有限差分数值方法应用于渔业和旅游管理问题。
Many emerging problems involve teams of agents taking part in a game. Such problems require a stochastic analysis with regard to the correlation structures among the agents belonging to a given team. In the context of Standard Borel spaces, this paper makes the following contributions for two teams of finitely many agents taking part in a zero-sum game: (i) An existence result will be presented for saddle-point equilibria in zero-sum games involving teams against teams when common randomness is assumed to be available in each team with an analysis on conditions for compactness of strategic tea…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards. The players are assumed to have infinite strategy spaces and the payoffs are assumed to be polynomials. In this paper we restrict our attention to a special class of games for which the single-controller assumption holds. It is shown that minimax equilibria and optimal strategies for such games may be obtained via semidefinite programming.
Paradoxes of Game Theoretic Equilibria and Price of Anarchy
研究博弈论均衡与无政府价格的悖论，指出将多智能体学习简化为静态均衡和黑箱后悔分析存在问题，通过分析内部纳什均衡、拥堵博弈等情况揭示相关不足，并研究非原子极限下的均衡变化，强调需重新评估基于动态的最坏情况均衡框架。
We study decentralized learning in two-player zero-sum discounted Markov games where the goal is to design a policy optimization algorithm for either agent satisfying two properties. First, the player does not need to know the policy of the opponent to update its policy. Second, when both players adopt the algorithm, their joint policy converges to a Nash equilibrium of the game. To this end, we construct a meta algorithm, dubbed as $\texttt{Homotopy-PO}$, which provably finds a Nash equilibrium at a global linear rate. In particular, $\texttt{Homotopy-PO}$ interweaves two base algorithms $\te…
Cooperation, Correlation and Competition in Ergodic N-player Games and Mean-field Games of Singular Controls: A Case Study
研究具有遍历性能准则的奇异控制N人博弈与均场博弈，探讨均场控制、粗相关均衡和Nash均衡三种最优性，通过Lagrange乘子法等方法显式计算并比较均衡，证明均场均衡可近似大规模N人博弈的合作与竞争均衡。
Ridesharing markets are complex: drivers are strategic, rider demand and driver availability are stochastic, and complex city-scale phenomena like weather induce large scale correlation across space and time. At the same time, past work has focused on a subset of these challenges. We propose a model of ridesharing networks with strategic drivers, spatiotemporal dynamics, and stochasticity. Supporting both computational tractability and better modeling flexibility than classical fluid limits, we use a two-level stochastic model that allows correlated shocks caused by weather or large public eve…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。