6533b837fe1ef96bd12a2ff3
RESEARCH PRODUCT
Mean-field games and two-point boundary value problems
Dario BausoAlessandro AstolfiThulasi Mylvaganamsubject
Stochastic partial differential equationDifferential equationMathematical analysisFree boundary problemFirst-order partial differential equationBoundary value problemHyperbolic partial differential equationNumerical partial differential equationsSeparable partial differential equationMathematicsdescription
A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-12-01 | 53rd IEEE Conference on Decision and Control |