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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 &#x201C;judge&#x201D; 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.

Max–Min Fair Sensor Scheduling: Game-Theoretic Perspective and Algorithmic Solution