A policy iteration method for Mean Field Games
نویسندگان
چکیده
The policy iteration method is a classical algorithm for solving optimal control problems. We introduce Mean Field Games systems and we prove, under monotonicity assumption on the coupling cost, convergence of this procedure to solution problem.
منابع مشابه
Softened Approximate Policy Iteration for Markov Games
This paper reports theoretical and empirical investigations on the use of quasi-Newton methods to minimize the Optimal Bellman Residual (OBR) of zero-sum two-player Markov Games. First, it reveals that state-of-the-art algorithms can be derived by the direct application of Newton’s method to different norms of the OBR. More precisely, when applied to the norm of the OBR, Newton’s method results...
متن کاملNumerical Method for Bertrand Mean Field Games Using Multigrid
We study dynamic Bertrand mean field games (MFG) with exhaustible capacities in which companies compete with each other using the price as the strategic variable and the interaction among the competition is through the average price. We consider both continuum mean field games and finite player games. Dynamic continuum mean field games can be modeled as a system of partial differential equation...
متن کاملMean-Field Games for Marriage
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple...
متن کاملPolicy iteration algorithm for zero-sum multichain stochastic games with mean payoff and perfect information
We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such a game can be characterized by a system of nonlinear equations, involving the mean payoff vector and an auxiliary vector (relative value or bias). We develop...
متن کاملMean Field Games
We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects. . . ). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited inform...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IFAC-PapersOnLine
سال: 2022
ISSN: ['2405-8963', '2405-8971']
DOI: https://doi.org/10.1016/j.ifacol.2022.11.087