Nonlinear Markov Control Processes and Games

The project was devoted to the analysis of a new class of stochastic games, nonlinear Markov games, as they arise as a (competitive) controlled version of nonlinear Markov processes, which can be characterized by the property that the future depends on the past via present position and its distribution. This class of games can model a variety of situations for economics and epidemics, statistical physics and pursuit- evasion processes. Another key motivation arises from the steady increase in complexity of the modem technological development requires an appropriate (or better optimal) management of complex stochastic systems consisting of large number of interacting components (agents, mechanisms, vehicles, subsidiaries, species, police units, etc) , which may have competitive or common interests. Under rather general assumptions, the limiting problem as the number of components tends to infinity can be described by a nonlinear evolution on measures, and its controlled version is given precisely by a nonlinear Markov control process or (in case of competitive interests) a nonlinear Markov game that we are investigating.