scholarly journals Markov-Nash equilibria in mean-field games with discounted cost

2017 ◽  
Author(s):  
Naci Saldi ◽  
Tamer Basar ◽  
Maxim Raginsky
Keyword(s):  
Nash Equilibria ◽  
Mean Field ◽  
Mean Field Games ◽  
Discounted Cost

scholarly journals Markov--Nash Equilibria in Mean-Field Games with Discounted Cost

2018 ◽  
Vol 56 (6) ◽  
pp. 4256-4287 ◽  
Author(s):  
Naci Saldi ◽  
Tamer Başar ◽  
Maxim Raginsky
Keyword(s):  
Nash Equilibria ◽  
Mean Field ◽  
Mean Field Games ◽  
Discounted Cost

scholarly journals Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria

2013 ◽  
Vol 24 (1) ◽  
pp. 93-115 ◽  
Author(s):  
Pierre Degond ◽  
Jian-Guo Liu ◽  
Christian Ringhofer
Keyword(s):  
Large Scale ◽  
Nash Equilibria ◽  
Mean Field ◽  
Mean Field Games

scholarly journals Nonzero-Sum Stochastic Games and Mean-Field Games with Impulse Controls

2021 ◽  
Author(s):  
Matteo Basei ◽  
Haoyang Cao ◽  
Xin Guo
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games ◽  
Mean Field ◽  
Sufficient Conditions ◽  
Mean Field Games ◽  
Model Parameters ◽  
Management Problem ◽  
Player Game ◽  
The Impact ◽  
Impulse Controls

We consider a general class of nonzero-sum N-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for the Nash equilibria (NEs) of the game. We then consider the limiting situation when N goes to infinity, that is, a suitable mean-field game (MFG) with impulse controls. We show that under appropriate technical conditions, there exists a unique NE solution to the MFG, which is an ϵ-NE approximation to the N-player game, with [Formula: see text]. As an example, we analyze in detail a class of two-player stochastic games which extends the classical cash management problem to the game setting. In particular, we present numerical analysis for the cases of the single player, the two-player game, and the MFG, showing the impact of competition on the player’s optimal strategy, with sensitivity analysis of the model parameters.

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