Sampled-Data Nash Equilibria in Differential Games with Impulse Controls

2021 ◽  
Vol 190 (3) ◽  
pp. 999-1022
Author(s):  
Utsav Sadana ◽  
Puduru Viswanadha Reddy ◽  
Tamer Başar ◽  
Georges Zaccour
Keyword(s):  
Differential Games ◽  
Nash Equilibria ◽  
Sampled Data ◽  
Impulse Controls

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.

scholarly journals A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models†

2017 ◽  
Vol 4 (3) ◽  
pp. 195-203 ◽  
Author(s):  
Alejandra Fonseca-Morales ◽  
◽  
Onésimo Hernández-Lerma
Keyword(s):  
Differential Games ◽  
Stochastic Models ◽  
Nash Equilibria ◽  
Pareto Optimal
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