We study a version of the multipopulation replicator dynamics, where each population is comprised of multiple subpopulations. We establish that correlated equilibrium is a natural solution concept in this setting. Specifically, we show that every correlated equilibrium is equivalent to a stationary state in the replicator dynamics of some subpopulation model. We also show that every interior st...

In this article, we consider the problem of equilibrium price formation in an incomplete securities market consisting one major financial firm and a large number minor firms. They carry out continuous trading via exchange to minimize their cost while facing idiosyncratic common noises as well stochastic order flows from individual clients. The process that balances demand supply securities, inc...

We study an equilibrium-based continuous asset pricing problem for the securities market. In previous work [M. Fujii and A. Takahashi (2022), SIAM J. Control Optim., 60, pp. 259--279], we have shown that a certain price process, which is given by solution to forward-backward stochastic differential equation of conditional McKean--Vlasov type, asymptotically clears market in large population lim...

Slope stability is one of the most important issues in open pit mining design. The main purpose of any open pit mine design is to propose an optimal excavation configuration, considering safety, ore recovery and financial return. An accurate pit slope design which accounts for the mine geology, structural geology, rock mass properties, and hydrogeology models of the mine area, drastically enhan...

In the paper, several different methods are adopted to control Lü system. With direct feedback method, Lü system can be stabilized at one equilibrium point or a limit cycle surrounding its equilibrium. With adaptive time-delayed feedback method, feedback coefficient and delay time can be adjusted adaptively to stabilize Lü system at its original unstable periodic orbit. With minimal energy meth...

A higher-order Godunov method for the radiation subsystem of radiation hydro-dynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation laws; it is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The method is second-o...

We consider a dynamic version of sender–receiver games, where the sequence of states follows an irreducible Markov chain observed by the sender. Under mild assumptions, we provide a simple characterization of the limit set of equilibrium payoffs, as players become very patient. Under these assumptions, the limit set depends on the Markov chain only through its invariant measure. The (limit) equ...

Abstract. This paper concerns the asymptotic behaviour of solutions of functional differential equations with unbounded delay to non–equilibrium limits. The underlying deterministic equation is presumed to be a linear Volterra integro–differential equation whose solution tends to a non–trivial limit. We show when the noise perturbation is bounded by a non–autonomous linear functional with a squ...