Recursively Decentralized Decision Making - Blackorby, Charles; Nissen, David; Primont, Daniel; Russell, R. Robert (Econometrica, 1974)
Decentralized decision making is consistent if it is executed without cost (i.e., without a loss of output or utility). Consistency requires that the objective function be appropriately structured. In this paper, a hierarchical decision making structure is rationalized by an objective function which combines some of the properties of homothetic separability and asymmetric separability. THIS PAPER EXAMINES consistent decentralized decision making in a hierarchical structure. The decision making process is rationalized by a class of objective functions which combines some of the properties of homothetic separability [1, 3] and recursive, or asymmetric, separability [5,8]. We refer to these functions as homothetically recursive. After introducing our basic notation and definitions, we prove a representation theorem for homothetically recursive functions in Section 1. In Section 2 we prove two duality theorems for homothetically recursive structures. A recursively decentralized decision making process, described in Section 3, is made manifest in the structure of the associated cost function. The analysis is carried out in the context of the theory of the firm but other applications are discussed briefly in Section 4.