Bertrand and Cournot Mean Field Games

By Patrick Chan, Ronnie Sircar. 2015

112 citations recorded by the source corpus.

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Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, methodology): “From Equation (4.19) and formula (4.2), we see that the market price is given by (4.20) k̄(s) = 2α− (1 + 2β)v̄(s) = α 1 + β − eµ(s−t) ( 1 + 2β 1 + β π(s)X̄(s) + α(1 + 2β) (1 + β)2 ∫ s t π(τ)dτ ) which, when using the model of Chan and Sircar [26] so that α = 1/2 and β = ǫ/2, becomes (4.21) k̄(s) = 1”
Mean Field Control and Mean Field Game Models with Several Populations (2018, background): “Some important applications can be found in finance [47, 4, 42, 18], economy [31, 29, 43, 19, 2, 28], systemic risk [27, 17], energy production [32, 20], or crowd motion [50, 44, 3].”
$N$-player games and mean-field games with absorption (2016, background): “In the applied literature, MFGs with absorption at zero have been recently considered in [8, 9] within the context of oligopolistic models with exhaustible resources.”
Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games (2015, methodology): “1) was introduced by Chan and Sircar in [9] to represent a mean field game in which producers compete to sell an exhaustible resource.”