Stochastic approximation and user adaptation in a competitive resource sharing system

This paper is motivated by the work of Altman and Shimkin (1998). Customers arrive at a service center and must choose between two types of service: a channel that is shared by all currently in it and a dedicated line. The mean service cost (or time) for any customer entering the shared resource depends on the decisions of all future arrivals up to the time of departure of that customer, and so has a competitive aspect. The decision rule of each arriving customer is based on its own immediate self-interest, given the available data on the past performance. If the current estimate of the cost for the shared resource equals that of the dedicated line, any decision is possible. The procedure is a type of learning algorithm. The convergence problem is one in asynchronous stochastic approximation, where the ODE may be a differential inclusion. It is shown that, asymptotically, the performance of the learning system is that for the symmetric Nash strategy, despite the allowed arbitrariness and lack of coordination