Abstract
This paper studies the linear-quadratic mean-field game (MFG) for a class of stochastic delayed systems. We consider a large-population system, where the dynamics of each agent is modeled by a stochastic differential delayed equation. The consistency condition is derived through an auxiliary system, which is an anticipated forward-backward stochastic differential equation with delay (AFBSDDE). The wellposedness of such an AFBSDDE system can be obtained using a continuation method. Thus, the MFG strategies can be defined on an arbitrary time horizon, not necessary on a small time horizon by a commonly used contraction mapping method. Moreover, the decentralized strategies are verified to satisfy the ϵ-Nash equilibrium property. For illustration, three special cases of delayed systems are further explored, for which the closed-loop and open-loop MFG strategies are derived, respectively.
| Original language | English |
|---|---|
| Pages (from-to) | 2722-2729 |
| Number of pages | 8 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 63 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 1 Aug 2018 |
Keywords
- Anticipated forward-backward stochastic differential equation with delay (AFBSDDE)
- continuation method
- input delay
- mean-field game (MFG)
- stochastic differential equation with delay (SDDE)
- ϵ-Nash equilibrium
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering