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We consider the design of a fair sensor schedule for a number of sensorsmonitoring different linear time-invariant processes. The largest averageremote estimation error among all processes is to be minimized. We firstconsider a general setup for the max-min fair allocation problem. Byreformulating the problem as its equivalent form, we transform the fairresource allocation problem into a zero-sum game between a "judge" and aresource allocator. We propose an equilibrium seeking procedure and show thatthere exists a unique Nash equilibrium in pure strategy for this game. We thenapply the result to the sensor scheduling problem and show that the max-minfair sensor scheduling policy can be achieved.

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