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-independe…
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48 results for “Markov Perfect equilibria”
New findings show pure strategy equilibria are more robust in a war of attrition game.
problem Analyzing a game of war of attrition under complete information.
method Examined the stability of equilibria in pure and mixed strategies under varying payoffs.
result Pure strategy equilibria are more robust to perturbations of the canonical model.
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.
New algorithms for RL in Markov games with independent linear function approximation, breaking the curse of multiagents.
problem Tackles the challenge of learning Markov equilibria in large state space Markov games with multiple agents.
method Proposes independent linear Markov games and designs new algorithms for learning Markov coarse correlated equilibria and Markov correlated equilibria with polynomial sample complexity.
result Breaks the curse of multiagents by achieving sample complexity bounds that scale polynomially with each agent's function class complexity.
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.
Algorithm minimizes regret and converges to equilibria in Markov games.
problem Regret minimization and convergence to equilibria in general-sum Markov games under adversarial opponents.
method Decentralized algorithm that uses policy optimization and controls path length to achieve sublinear regret.
result Sublinear regret guarantees for convergence to correlated equilibrium in Markov games.
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.
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through …
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …
This paper tackles sample-efficient reinforcement learning for partially observable Markov games.
problem Learning in partially observable Markov games with incomplete information.
method A simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) for self-play, and a variant of optimistic MLE for adversarial opponents.
result The proposed algorithms achieve approximate Nash, correlated, and coarse correlated equilibria in polynomial samples for weakly revealing POMGs.
Sample-Efficient Robust Multi-Agent Reinforcement Learning in the Face of Environmental Uncertaintycs.LG
This work tackles robust RL in multi-agent settings, improving sample efficiency.
problem Overcoming environmental uncertainties in multi-agent reinforcement learning.
method Proposes DRNVI, a sample-efficient algorithm for learning robust equilibria in RMGs.
result Establishes near-optimal sample complexity for solving RMGs.
New approach tackles non-stationary multi-agent games with black-box methods.
problem Challenges in learning equilibria in non-stationary multi-agent systems.
method Versatile black-box approach applicable to various games, including general-sum, potential, and Markov games.
result Achieves optimal regret bounds for non-stationary games, with or without knowledge of total variation.
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.
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.
Study efficient offline RL in Markov games with general models.
problem Learn approximate equilibria from offline data in Markov games.
method Use Bellman-consistent pessimism for interval estimation and optimize gap relaxation.
result First framework for sample-efficient offline learning in Markov games, handling all equilibria.
Game theory helps analyze ESOs/EBIs in production and service sectors.
problem Economic incentives affect traditional production/service functions and create intangible capital.
method Uses game theory to analyze interactions in ESO/EBI transactions.
result No perfect Nash Equilibria for two-stage games involving many participants.
Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with curren…
Method locates equilibria on unknown Riemannian manifolds using iterative sampling and parallel transport.
problem Locating equilibria on unknown Riemannian manifolds defined by point-clouds.
method Iterative sampling, parallel transport, and generalized isoclines.
result Algorithm reliably locates equilibria of dynamical systems on unknown manifolds.
This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switch according to a finite…
Given a hyperbolic domain, the nearest point retraction is a conformally natural homotopy equivalence from the domain to the boundary of the convex core of its complement. Marden and Markovic showed that if the domain is uniformly perfect, then there exists a conformally natural quasiconformal map which admits a bounde…
The paper analyzes strategic irreversible investments with novel dynamic strategies.
problem Tradeoff between preemption incentives and option value of waiting in oligopolistic markets.
method Developed novel Markov perfect equilibrium to handle singular control of optimal investment.
result Simpler strategies lead to a 'preemption trap' with zero net present values.
New MARL algorithms resolve the curse of multiagency with function approximation.
problem Challenges in Multi-Agent Reinforcement Learning (MARL) due to the curse of multiagency.
method V-Learning with Policy Replay and Decentralized Optimistic Policy Mirror Descent.
result First polynomial sample complexity results for learning approximate Coarse Correlated Equilibria (CCEs) of Markov Games under decentralized linear function approximation.
A family of Markov blankets in a faithful Bayesian network satisfies the symmetry and consistency properties. In this paper, we draw a bijection between families of consistent Markov blankets and moral graphs. We define the new concepts of weak recursive simpliciality and perfect elimination kits. We prove that they ar…
Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to cons…
We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain in the Riemann sphere to the boundary of the convex hull of its complement. As a corollary, one obtains explicit bounds on the quasi-isometry constant of the nearest point retraction with respect to the…
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…
There is an increasing demand for computing the relevant structures, equilibria and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension red…
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
The paper addresses dynamic capital structure models with defaultable debt, proving existence and uniqueness.
problem Dynamic capital structure models with an investor break-even condition may not generate a contraction mapping.
method Provided an example and used a dual problem and change of measure to prove existence and uniqueness.
result A unique Markov-perfect equilibrium exists where firm decisions reflect state-dependent targets.
This paper improves sample efficiency for learning equilibria in multi-player games.
problem Sample-efficient learning of equilibria in games with many players.
method Designs algorithms for learning CCE and CE with polynomial sample complexity in the number of players.
result First to show polynomial sample complexity for learning CCE and CE in multi-player games.
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…
Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. We present formulations of inference problems in Markov random f…
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.
Counterfactual Regret Minimization (CFR) has found success in settings like poker which have both terminal states and perfect recall. We seek to understand how to relax these requirements. As a first step, we introduce a simple algorithm, local no-regret learning (LONR), which uses a Q-learning-like update rule to allo…
The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
problem Characterizing and comparing different types of equilibria for time-inconsistent stopping problems.
method Analyzes log sub-additive discount functions and one-dimensional diffusion processes to derive necessary and sufficient conditions for weak equilibria and other types of equilibria.
result Conditions for weak equilibria and their implications for other types of equilibria are provided.
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…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
Paper develops efficient algorithms for learning rationalizable equilibria in multiplayer games.
problem Learning rationalizable behavior in multiplayer games under bandit feedback.
method New algorithms for finding rationalizable Coarse Correlated Equilibria and Correlated Equilibria with polynomial sample complexity.
result Achieved polynomial sample complexity for learning rationalizable equilibria, improving over existing exponential complexity.
Study global geometry of dynamical systems with entire vector fields.
problem Understanding the global structure of equilibria and their basins.
method Step-by-step analysis of basins of centers, nodes, and foci; introduction of global elliptic sectors.
result Characterization of heteroclinic regions connecting equilibria.
Imitation learning algorithms can be used to learn a policy from expert demonstrations without access to a reward signal. However, most existing approaches are not applicable in multi-agent settings due to the existence of multiple (Nash) equilibria and non-stationary environments. We propose a new framework for multi-…
V-learning tackles multiagent reinforcement learning by reducing sample complexity.
problem Curse of multiagents in multiagent reinforcement learning.
method V-learning is a fully decentralized algorithm that learns Nash, correlated, and coarse correlated equilibria.
result V-learning achieves sample complexity that scales with the maximum number of actions per agent, not the joint action space.
New results on financial equilibria in markets with general semimartingales.
problem Existence and uniqueness of mean-variance equilibria in semimartingale markets.
method Analysis of dynamic mean-variance hedging and fixed-point problems.
result First results allowing for general semimartingales and both discrete and continuous time.
We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof is also useful in studying the bifurcation of relative equilibria.
Equilibria analysis of a networked bivirus epidemic model using Poincaré--Hopf and Manifold Theorymath.DS
This paper analyzes complex equilibria in a networked bivirus epidemic model.
problem Identify conditions for coexistence equilibria in a networked bivirus model.
method Employ Poincaré-Hopf Theorem with modifications and Morse inequalities.
result Establish properties on the local stability/instability of coexistence equilibria.
Perceptual Kalman Filters: Online State Estimation under a Perfect Perceptual-Quality Constraintcs.LG
Perceptual Kalman filters maintain human-perceptual quality while processing data.
problem Maintaining human-perceptual quality in signal processing under temporal constraints.
method An optimal causal filtering approach under a perfect perceptual-quality constraint.
result Adding perceptual quality constraints introduces a dilemma that requires sacrificing MSE for temporal consistency.
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
New method for MCMC models without perfect or sequential samplers.
problem Bayesian inference for complex models with intractable terms.
method Utilizes tractable independence model to construct unbiased estimates.
result Scalable method for high-dimensional models.