Uncertain production environment and communication structure

Pongou and Tondji (Pongou and Tondji, Games and Economic Behavior, 108, 206-224, 2018) describe 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, the authors 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 enabled them to bring forth a solution named 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 an uncertain production environment. By defining some intuitive axioms, we solve the problem of valuing inputs in Pongou and Tondji’s (2018) environment, and improve it with 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 MyersonR value, or the Bayesian Myerson value, and its individual rational revision called the Bayesian MyersonR value. Furthermore, we generalize the core to this environment.