scholarly journals Long Time Average of First Order Mean Field Games and Weak KAM Theory

2013 ◽  
Vol 3 (4) ◽  
pp. 473-488 ◽  
Author(s):  
P. Cardaliaguet
Keyword(s):  
Kam Theory ◽  
Mean Field ◽  
Mean Field Games ◽  
Weak Kam Theory ◽  
First Order ◽  
Long Time ◽  
Time Average

scholarly journals Weak KAM Approach to First-Order Mean Field Games with State Constraints

2021 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Wei Cheng ◽  
Cristian Mendico ◽  
Kaizhi Wang
Keyword(s):  
Time Horizon ◽  
State Constraints ◽  
Kam Theory ◽  
Mean Field ◽  
Mean Field Games ◽  
Asymptotic Behavior Of Solutions ◽  
Weak Kam Theory ◽  
First Order ◽  
Jacobi Equations ◽  
Ergodic Mean

AbstractWe study the asymptotic behavior of solutions to the constrained MFG system as the time horizon T goes to infinity. For this purpose, we analyze first Hamilton–Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on [0, T] converges to the solution of the ergodic system as T goes to infinity.

scholarly journals Long-Time Behavior of First-Order Mean Field Games on Euclidean Space

2019 ◽  
Vol 10 (2) ◽  
pp. 361-390
Author(s):  
Piermarco Cannarsa ◽  
Wei Cheng ◽  
Cristian Mendico ◽  
Kaizhi Wang
Keyword(s):  
Euclidean Space ◽  
Mean Field ◽  
Mean Field Games ◽  
Time Behavior ◽  
Long Time Behavior ◽  
First Order ◽  
Long Time

scholarly journals Long time average of mean field games

2012 ◽  
Vol 7 (2) ◽  
pp. 279-301 ◽  
Author(s):  
Pierre Cardaliaguet ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions ◽  
Alessio Porretta
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Long Time ◽  
Time Average

Long Time Average of Mean Field Games with a Nonlocal Coupling

2013 ◽  
Vol 51 (5) ◽  
pp. 3558-3591 ◽  
Author(s):  
P. Cardaliaguet ◽  
J.-M. Lasry ◽  
P.-L. Lions ◽  
A. Porretta
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Nonlocal Coupling ◽  
Long Time ◽  
Time Average

A Nonstationary Hidden Markov Model with Approximately Infinitely-Long Time-Dependencies

2016 ◽  
Vol 25 (05) ◽  
pp. 1640001 ◽  
Author(s):  
Sotirios Chatzis ◽  
Dimitrios Kosmopoulos ◽  
George Papadourakis
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
Mean Field ◽  
Sequential Data ◽  
First Order ◽  
Order Markov Chain ◽  
Inference Algorithms ◽  
Unrealistic Assumption ◽  
Long Time ◽  
Time Dependencies

Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first-order Markov chain. In other words, only one-step back dependencies are modeled which is a rather unrealistic assumption in most applications. In this paper, we propose a method for postulating HMMs with approximately infinitely-long time-dependencies. Our approach considers the whole history of model states in the postulated dependencies, by making use of a recently proposed nonparametric Bayesian method for modeling label sequences with infinitely-long time dependencies, namely the sequence memoizer. We manage to derive training and inference algorithms for our model with computational costs identical to simple first-order HMMs, despite its entailed infinitely-long time-dependencies, by employing a mean-field-like approximation. The efficacy of our proposed model is experimentally demonstrated.

scholarly journals First-order, stationary mean-field games with congestion

2018 ◽  
Vol 173 ◽  
pp. 37-74 ◽  
Author(s):  
David Evangelista ◽  
Rita Ferreira ◽  
Diogo A. Gomes ◽  
Levon Nurbekyan ◽  
Vardan Voskanyan
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
First Order

scholarly journals Viability analysis of the first-order mean field games

2020 ◽  
Vol 26 ◽  
pp. 33
Author(s):  
Yurii Averboukh
Keyword(s):  
Mean Field ◽  
Initial Distribution ◽  
Initial Time ◽  
Mean Field Games ◽  
Sufficient Condition ◽  
Mean Field Game ◽  
First Order ◽  
Viability Analysis ◽  
A Value ◽  
Object Of Study

In the paper, we examine the dependence of the solution of the deterministic mean field game on the initial distribution of players. The main object of study is the mapping which assigns to the initial time and the initial distribution of players the set of expected rewards of the representative player corresponding to solutions of mean field game. This mapping can be regarded as a value multifunction. We obtain the sufficient condition for a multifunction to be a value multifunction. It states that if a multifunction is viable with respect to the dynamics generated by the original mean field game, then it is a value multifunction. Furthermore, the infinitesimal variant of this condition is derived.

scholarly journals The selection problem for some first-order stationary Mean-field games

2020 ◽  
Vol 15 (4) ◽  
pp. 681-710
Author(s):  
Diogo A. Gomes ◽  
◽  
Hiroyoshi Mitake ◽  
Kengo Terai ◽  
Keyword(s):  
Mean Field ◽  
Selection Problem ◽  
Mean Field Games ◽  
First Order
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