Guaranteed performance regions in Markovian systems with competing decision makers

A decision maker is facing a dynamic system which is being controlled by himself/herself as well as by other decision makers. He/she considers a vector of performance measures. Acceptable performance is defined through a set in the space of performance vectors. Whether this decision maker can guarantee a (time-averaged) performance vector which approaches this desired set is considered for the worst-case scenario, in which other decision makers may, for selfish reasons, try to exclude his/her vector from the desired set. For a controlled Markov model of the system, a sufficient condition for approachability is given, and appropriate control strategies are constructed. Under certain recurrence conditions, a complete characterization of approachability is then provided for convex sets. The mathematical formulation leads to a theory of approachability for stochastic games with vector payoffs. A simple queuing example illustrates this approach