Uncertain production environment and communication structure: the Bayesian Myerson value

Abstract

Pongou and Tondji (Pongou and Tondji, Games and Economic Behavior, 108, 206-224, 2018) described an uncertain production environment as a situation where input supply is uncertain. Each input has a finite set of actions, and uncertainty is formalized as a probability distribution over this set. These inputs can be workers in a firm, vertices in a networked economy, securities in a financial market, etc. Then they examined the problem of valuing inputs in that environment. By using axiomatic methods, they provided a solution called the a priori Shapley value. Knowing the output level, they provided a solution called the Bayesian Shapley value. In this paper, we examine some applications of the Myerson value (Myerson, Mathematics of Operations Research, 2, 225-229, 1977) in the field of uncertain production environment. By defining some intuitive axioms, we solve the problem of valuing inputs in Pongou and Tondji's (2018) environment enriched by a communication structure. Depending on the information structure, this leads to the a priori Myerson value and its individual rational revision called the a priori Myerson R value, or the Bayesian Myerson value and its individual rational revision called the Bayesian Myerson R value. Furthermore, we introduce the notion of the core in this environment.