Dynamics on Linear Influence Network Games Under Stochastic Environments

Zhengyuan Zhou, Nicholas Bambos, Peter W. Glynn

Abstract: A linear influence network is a broadly applicable conceptual framework in risk management. It has important applications in computer and network security. Prior work on linear influence networks targeting those risk management applications have been focused on equilibrium analysis in a static, one-shot setting. Furthermore, the underlying network environment is also assumed to be deterministic. In this paper, we lift those two assumptions and consider a formulation where the network environment is stochastic and time-varying. In particular, we study the stochastic behavior of the well-known best response dynamics. Specifically, we give interpretable and easily verifiable sufficient conditions under which we establish the existence and uniqueness of as well as convergence (with exponential convergence rate) to a stationary distribution of the corresponding Markov chains.