A Generic Mean Field Convergence Result for Systems of Interacting Objects

We consider a model for interacting objects, where the evolution of each object is given by a finite state Markov chain, whose transition matrix depends on the present and the past of the distribution of states of all objects. This is a general model of wide applicability; we mention as examples: TCP connections, HTTP flows, robot swarms, reputation systems. We show that when the number of objects is large, the occupancy measure of the system converges to a deterministic dynamical system (the “mean field”) with dimension the number of states of an individual object. We also prove a fast simulation result, which allows to simulate the evolution of a few particular objects imbedded in a large system. We illustrate how this can be used to model the determination of reputation in large populations, with various liar strategies.

• Type: Conference
• Year: 2007
• Where: QEST
• Authors: Jean-Yves Le Boudec, David McDonald, Jochen Mundinger
• Keywords: Model, QEST 2007, Quantitative Evaluation Of Systems, State Markov Chain, Various Liar Strategies