One of the contributions of this chapter is a method based on game theory to study when companies prefer a replenishment policy. Technically, it has several contributions, such as the method that depends on attitudes towards risk and client satisfaction, and the definition of a cost at risk (CaR) based on a performance indicator called value at risk (VaR). The chapter illustrates the methods with a case study comparing three different replenishment policies. Here, α is a representative of traditional replenishment policies based on optimization and using no information sharing (IS), β is a policy designed to reduce the bullwhip effect by exploiting slow IS, and γ is an improvement on β in which IS is instantaneous. The motivation for applying the method to compare α, β and γ is the comparison of two different paradigms: optimization and stream management. The chapter discusses the results obtained with these three policies.