Fair allocation of sensor measurements using Shapley value

In this paper, we consider the problem of measurement allocation in a spatially correlated sensor field. Our objective is to determine the probability of each sensor´s being measured for improved observability; the sensor located at less correlated area should be assigned more probability. To this end, we quantify the level of correlation of each sensor through the mutual information criterion reflecting the level of uncertainty about unattended locations. Then we deploy the Shapley value, a representative single-valued solution concept in cooperative game theory. The Shapley value expresses the average marginal contribution of each sensor to the observation of a spatially correlated sensor field, and can be used to allocate the probability of each sensor´s being measured in proportion to its contribution. Against the intractability in computing the true Shapley value, we deploy a randomized methods based on sampling, which can compute the approximate Shapley value with linear time complexity. Through numerical experiments, we evaluate the approximate Shapley value achieved by the randomized method by comparing it to the exact Shapley value, and estimate how the measurement allocation based on the Shapley value contributes to the overall observability and coverage.