Games with incomplete information: A simplified exposition with inventory management applications

In most existing literature in supply chain management it is assumed that the players possess complete information about the game, i.e., the players' payoff (objective) functions are assumed to be common knowledge. For static and dynamic games with complete information, the Nash equilibrium and subgame perfect equilibrium are the standard solution concepts, respectively. For static and dynamic games with incomplete information, the Bayesian Nash equilibrium and perfect Bayesian equilibrium, respectively, are used as solution concepts. After presenting a brief review of the static and dynamic games under complete information, the application of these two games in inventory management is illustrated by using a single-period stochastic inventory problem with two competing newsvendors. Next, we illustrate the Bayesian Nash and perfect Bayesian equilibrium solution concepts for the static and dynamic games under incomplete information with two competing newsvendors. The expository nature of our paper may help researchers in inventory/supply chain management gain easy access to the complicated notions related to the games played under incomplete information. ► Incomplete information games are competitive situations where the players' objectives are not common knowledge. ► This paper presents a tutorial on such games and considers static and dynamic games of incomplete information. ► For static games, the solution concepts is Bayesian Nash and for dynamic games it is perfect Bayesian equilibrium. ► We use stochastic inventory models to illustrate the solution concepts.