  We consider the design of a fair sensor schedule for a number of sensors
monitoring different linear time-invariant processes. The largest average
remote estimation error among all processes is to be minimized. We first
consider a general setup for the max-min fair allocation problem. By
reformulating the problem as its equivalent form, we transform the fair
resource allocation problem into a zero-sum game between a "judge" and a
resource allocator. We propose an equilibrium seeking procedure and show that
there exists a unique Nash equilibrium in pure strategy for this game. We then
apply the result to the sensor scheduling problem and show that the max-min
fair sensor scheduling policy can be achieved.
