相关论文: Value Iteration Algorithm for Mean-field Games

We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while…

Value iteration is a fundamental algorithm for solving Markov Decision Processes (MDPs). It computes the maximal $n$-step payoff by iterating $n$ times a recurrence equation which is naturally associated to the MDP. At the same time, value…

Mean field game facilitates analyzing multi-armed bandit (MAB) for a large number of agents by approximating their interactions with an average effect. Existing mean field models for multi-agent MAB mostly assume a binary reward function,…

Equilibrium computation in markets usually considers settings where player valuation functions are known. We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of…

We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…

This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide…

This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxed control formulation, we first establish the martingale…

Value iteration is a commonly used and empirically competitive method in solving many Markov decision process problems. However, it is known that value iteration has only pseudo-polynomial complexity in general. We establish a somewhat…

We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our primary method employs a version of the double oracle, iteratively adding strategies…

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

This paper establishes that an MDP with a unique optimal policy and ergodic associated transition matrix ensures the convergence of various versions of the Value Iteration algorithm at a geometric rate that exceeds the discount factor…

A decentralized blockchain is a distributed ledger that is often used as a platform for exchanging goods and services. This ledger is maintained by a network of nodes that obeys a set of rules, called a consensus protocol, which helps to…

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…

Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…

Mean-payoff games are important quantitative models for open reactive systems. They have been widely studied as games of full observation. In this paper we investigate the algorithmic properties of several sub-classes of mean-payoff games…

This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the…

This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…

We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not…