The equivalence of team theory's integral equations and a Cauchy system: sensitivity analysis of a variational problem

Team decision theory studies the problem of how a group of decision makers should use information to coordinate their actions. Mathematically, the task is to find functions that maximize an objective functional. The Euler equations take the form of a system of integral equations. In this paper, it will be shown that a class of such integral equations has solutions that are identical to the solutions of a system of initial-valued integrodifferential equations. This Cauchy system describes the sensitivity of the solutions to underlying parameters and provides an efficient technique for solving difficult team decision problems. An analysis of a profit maximizing firm demonstrates the usefulness of the Cauchy system.