A multidimensional comparison theorem for solutions of the Skorokhod problem in a wedge with applications to control of a group of independent identical agents

A problem of controlling a group of independent identical agents is considered. Such problems arise in mathematical economics, in robotics (swarms of mini-robots). The model includes a stochastic component. The general method of the Bellman equation cannot be applied to this problem. The solution is found by the comparison method for solutions of stochastic differential equations using the technique of the Skorokhod reflection operators. The optimal policy admits a realization as a decentralized group control algorithm.