Discrete-time decentralized control using the risk-sensitive performance criterion in the large population regime: A mean field approach

2015 ◽  
Author(s):  
Jun Moon ◽  
Tamer Basar
Keyword(s):  
Decentralized Control ◽  
Discrete Time ◽  
Large Population ◽  
Mean Field ◽  
Performance Criterion ◽  
Field Approach ◽  
Risk Sensitive

scholarly journals A mean field approach for optimization in discrete time

2010 ◽  
Vol 21 (1) ◽  
pp. 63-101 ◽  
Author(s):  
Nicolas Gast ◽  
Bruno Gaujal
Keyword(s):  
Discrete Time ◽  
Mean Field ◽  
Field Approach

Discrete-Time Control for Systems of Interacting Objects with Unknown Random Disturbance Distributions: A Mean Field Approach

2015 ◽  
Vol 74 (1) ◽  
pp. 197-227 ◽  
Author(s):  
Carmen G. Higuera-Chan ◽  
Héctor Jasso-Fuentes ◽  
J. Adolfo Minjárez-Sosa
Keyword(s):  
Discrete Time ◽  
Mean Field ◽  
Random Disturbance ◽  
Field Approach ◽  
Time Control

scholarly journals Replica-mean-field limits of fragmentation-interaction-aggregation processes

2022 ◽  
pp. 1-22
Author(s):  
François Baccelli ◽  
Michel Davydov ◽  
Thibaud Taillefumier
Keyword(s):  
Point Process ◽  
Discrete Time ◽  
Infinite Number ◽  
Mean Field ◽  
Asymptotic Independence ◽  
State Variables ◽  
Field Approach ◽  
Aggregation Processes ◽  
Mean Field Limits ◽  
Time Point

Abstract Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called ‘Poisson hypothesis’. However, in most applications this hypothesis is only conjectured. In this paper we establish the Poisson hypothesis for a general class of discrete-time, point-process-based dynamics that we propose to call fragmentation-interaction-aggregation processes, and which are introduced here. These processes feature a network of nodes, each endowed with a state governing their random activation. Each activation triggers the fragmentation of the activated node state and the transmission of interaction signals to downstream nodes. In turn, the signals received by nodes are aggregated to their state. Our main contribution is a proof of the Poisson hypothesis for the replica-mean-field version of any network in this class. The proof is obtained by establishing the propagation of asymptotic independence for state variables in the limit of an infinite number of replicas. Discrete-time Galves–Löcherbach neural networks are used as a basic instance and illustration of our analysis.

scholarly journals ONE DIMENSIONAL ASYNCHRONOUS COOPERATIVE PARRONDO'S GAMES

2003 ◽  
Vol 03 (04) ◽  
pp. L389-L398 ◽  
Author(s):  
ZORAN MIHAILOVIĆ ◽  
MILAN RAJKOVIĆ
Keyword(s):  
Computer Simulation ◽  
Markov Chain ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Mean Field ◽  
Discrete Time Markov Chain ◽  
One Dimensional ◽  
Field Approach ◽  
The Mean ◽  
The One

A discrete-time Markov chain solution with exact rules for general computation of transition probabilities of the one-dimensional cooperative Parrondo's games is presented. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.

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.

scholarly journals Inhomogeneous mean-field approach to collective excitations near the superfluid-Mott glass transition

2021 ◽  
pp. 168526
Author(s):  
Martin Puschmann ◽  
João C. Getelina ◽  
José A. Hoyos ◽  
Thomas Vojta
Keyword(s):  
Glass Transition ◽  
Mean Field ◽  
Collective Excitations ◽  
Field Approach

scholarly journals A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

2021 ◽  
Author(s):  
Stefano Almi ◽  
Marco Morandotti ◽  
Francesco Solombrino
Keyword(s):  
Mean Field ◽  
Evolutionary Games ◽  
Type Systems ◽  
Convergence Result ◽  
Performance Criterion ◽  
Mean Field Limit ◽  
Spatially Inhomogeneous ◽  
Convergence Results ◽  
Special Cases ◽  
Lagrangian Scheme

AbstractA multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.

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