Stochastic Graphon Games: II. The Linear-Quadratic Case

In this paper, we analyze linear-quadratic stochastic differential games with a continuum of players interacting through graphon aggregates, each state being subject to idiosyncratic Brownian shocks. The major technical issue is the joint measurability of the player state trajectories with respect t...

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Vydané v:Applied mathematics & optimization Ročník 85; číslo 3
Hlavní autori: Aurell, Alexander, Carmona, René, Laurière, Mathieu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.06.2022
Springer Nature B.V
Predmet:
Aggregates
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Control
Control theory
Differential equations
Differential games
Equations of state
Equilibrium conditions
Game theory
Macroeconomics
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Maximum principle
Numerical and Computational Physics
Optimization
Players
Random variables
Simulation
Systems Theory
Theoretical
60H10
60H20
Exact law of large numbers
91A15
Fubini extensions
91A07
Continuum of players
Graphons
Stochastic differential games
ISSN:0095-4616, 1432-0606
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Popis
Shrnutí:In this paper, we analyze linear-quadratic stochastic differential games with a continuum of players interacting through graphon aggregates, each state being subject to idiosyncratic Brownian shocks. The major technical issue is the joint measurability of the player state trajectories with respect to samples and player labels, which is required to compute for example costs involving the graphon aggregate. To resolve this issue we set the game in a Fubini extension of a product probability space. We provide conditions under which the graphon aggregates are deterministic and the linear state equation is uniquely solvable for all players in the continuum. The Pontryagin maximum principle yields equilibrium conditions for the graphon game in the form of a forward-backward stochastic differential equation, for which we establish existence and uniqueness. We then study how graphon games approximate games with finitely many players over graphs with random weights. We illustrate some of the results with a numerical example.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-022-09839-2