$\epsilon$-Nash Equilibria for Partially Observed LQG Mean Field Games With a Major Player

2017 ◽  
Vol 62 (7) ◽  
pp. 3225-3234 ◽  
Author(s):  
Peter E. Caines ◽  
Arman C. Kizilkale
Keyword(s):  
Nash Equilibria ◽  
Mean Field ◽  
Mean Field Games ◽  
Major Player ◽  
Partially Observed

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 Price Formation and Optimal Trading in Intraday Electricity Markets with a Major Player

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 133
Author(s):  
Olivier Féron ◽  
Peter Tankov ◽  
Laura Tinsi
Keyword(s):  
Nash Equilibrium ◽  
Electricity Markets ◽  
Mean Field ◽  
Optimal Strategies ◽  
Price Formation ◽  
Mean Field Games ◽  
Optimal Trading ◽  
Major Player ◽  
Major Producer ◽  
Small Producers

We study price formation in intraday electricity markets in the presence of intermittent renewable generation. We consider the setting where a major producer may interact strategically with a large number of small producers. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in a closed form in the asymptotic framework of mean field games with a major player.

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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