On viscosity solutions of path-dependent Hamilton--Jacobi--Bellman--Isaacs equations for fractional-order systems

Gomoyunov, Mikhail I.

doi:10.48550/arxiv.2109.02451

Cited by 2 publications

(1 citation statement)

References 16 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned above, two problems must be considered. The first is optimizing this system by invoking Bellman dynamic programming theorem, Pontryagain's stochastic optimization theorem, and Fleming theorem, then transferring the optimal problem to a corresponding Hamilton-Jacobi-Isaacs equation, which has been resolved respectively by Chighoub et al [10], Guo et al [11], Gomoyunov [12]. The second one is constructing a payoff distribution procedure for all agents [13,14].…”

Section: Behavior and The Equilibrium Of The Agent In Multi-local-wor...mentioning

confidence: 99%

Optimal Strategies Trajectory with Multi-Local-Worlds Graph

Wang¹,

Zheng²,

Zeng³

et al. 2023

Computers, Materials &Amp; Continua

View full text Add to dashboard Cite

This paper constructs a non-cooperative/cooperative stochastic differential game model to prove that the optimal strategies trajectory of agents in a system with a topological configuration of a Multi-Local-World graph would converge into a certain attractor if the system's configuration is fixed. Due to the economics and management property, almost all systems are divided into several independent Local-Worlds, and the interaction between agents in the system is more complex. The interaction between agents in the same Local-World is defined as a stochastic differential cooperative game; conversely, the interaction between agents in different Local-Worlds is defined as a stochastic differential non-cooperative game. We construct a non-cooperative/cooperative stochastic differential game model to describe the interaction between agents. The solutions of the cooperative and noncooperative games are obtained by invoking corresponding theories, and then a nonlinear operator is constructed to couple these two solutions together. At last, the optimal strategies trajectory of agents in the system is proven to converge into a certain attractor, which means that strategies trajectory are certainty as time tends to infinity or a large positive integer. It is concluded that the optimal strategy trajectory with a nonlinear operator of cooperative/noncooperative stochastic differential game between agents can make agents in a certain Local-World coordinate and make the Local-World payment maximize, and can make the all Local-Worlds equilibrated; furthermore, the optimal strategy of the coupled game can converge into a particular attractor that decides the optimal property.

show abstract