Remote estimation games over shared networks

Consider a system that is formed by two sensors, which measure a random variable each, and two remote estimators. Each estimator is tasked to produce an estimate of one of the variables based on information sent to it by its corresponding sensor. We propose a new class of problems in which information is transmitted from the sensors to the estimators via a collision channel with and without capture. Our results characterize the structure of the policies that are in Nash equilibrium or are secure in a well-defined sense.