scholarly journals Large deviations principle for discrete-time mean-field games

2021 ◽  
Vol 157 ◽  
pp. 105042
Author(s):  
Naci Saldi
Keyword(s):  
Large Deviations ◽  
Discrete Time ◽  
Mean Field ◽  
Mean Field Games ◽  
Large Deviations Principle

scholarly journals Discrete-time mean field games with risk-averse agents

2021 ◽  
Author(s):  
Joseph Frédéric Bonnans ◽  
Pierre Lavigne ◽  
Laurent Pfeiffer
Keyword(s):  
Discrete Time ◽  
Risk Measures ◽  
Mean Field ◽  
Dynamic Game ◽  
Coupled System ◽  
Kolmogorov Equation ◽  
Mean Field Games ◽  
Risk Averse ◽  
Existence Of A Solution ◽  
Approximate Nash Equilibrium

We propose and investigate a discrete-time mean field game model involving risk-averse agents. The model under study is a coupled system of dynamic programming equations with a Kolmogorov equation. The agents' risk aversion is modeled by composite risk measures. The existence of a solution to the coupled system is obtained with a fixed point approach. The corresponding feedback control allows to construct an approximate Nash equilibrium for a related dynamic game with finitely many players.

scholarly journals Discrete time mean field games: The short-stage limit

2015 ◽  
Vol 2 (1) ◽  
pp. 89-101
Author(s):  
Juan Pablo Maldonado López
Keyword(s):  
Discrete Time ◽  
Mean Field ◽  
Mean Field Games

scholarly journals Multipopulation Spin Models: A View from Large Deviations Theoretic Window

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Alex Akwasi Opoku ◽  
Godwin Osabutey
Keyword(s):  
Large Deviations ◽  
Probability Distributions ◽  
Mean Field ◽  
Variational Formula ◽  
Rate Function ◽  
Large Deviations Principle ◽  
Spin Models ◽  
Empirical Measures ◽  
Rate Functions ◽  
Empirical Means

This paper studies large deviations properties of vectors of empirical means and measures generated as follows. Consider a sequence X1,X2,…,Xn of independent and identically distributed random variables partitioned into d-subgroups with sizes n1,…,nd. Further, consider a d-dimensional vector mn whose coordinates are made up of the empirical means of the subgroups. We prove the following. (1) The sequence of vector of empirical means mn satisfies large deviations principle with rate n and rate function I, when the sequence X1,X2,…,Xn is Rl valued, with l≥1. (2) Similar large deviations results hold for the corresponding sequence of vector of empirical measures Ln if Xi’s, i=1,2,…,n, take on finitely many values. (3) The rate functions for the above large deviations principles are convex combinations of the corresponding rate functions arising from the large deviations principles of the coordinates of mn and Ln. The probability distributions used in the convex combinations are given by α=(α1,…,αd)=limn→∞1/n(n1,…,nd). These results are consequently used to derive variational formula for the thermodynamic limit for the pressure of multipopulation Curie-Weiss (I. Gallo and P. Contucci (2008), and I. Gallo (2009)) and mean-field Pott’s models, via a version of Varadhan’s integral lemma for an equicontinuous family of functions. These multipopulation models serve as a paradigm for decision-making context where social interaction and other socioeconomic attributes of individuals play a crucial role.

Approximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field Games

2020 ◽  
Vol 45 (4) ◽  
pp. 1596-1620
Author(s):  
Naci Saldi ◽  
Tamer Başar ◽  
Maxim Raginsky
Keyword(s):  
Discrete Time ◽  
Empirical Distribution ◽  
Infinite Horizon ◽  
Mean Field ◽  
Mean Field Games ◽  
Infinite Population ◽  
Approximate Nash Equilibrium ◽  
Risk Sensitive ◽  
The Mean ◽  
Sensitive Optimality

In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive optimality criterion. Risk sensitivity is introduced for each agent (player) via an exponential utility function. In this game model, each agent is coupled with the rest of the population through the empirical distribution of the states, which affects both the agent’s individual cost and its state dynamics. Under mild assumptions, we establish the existence of a mean-field equilibrium in the infinite-population limit as the number of agents (N) goes to infinity, and we then show that the policy obtained from the mean-field equilibrium constitutes an approximate Nash equilibrium when N is sufficiently large.

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