T This paper analyzes different pricing strategies in a two-echelon supply chain including one supplier and two retailers. The supplier and the retailers face random yield and random demand, respectively. Moreover, coordination or non-coordination of retailers in receiving the discount is investigated. Game theory is used to model and analyze the problems. The supplier as a leader of Stackelbe...

In this entry we characterize pricing kernels or stochastic discount factors that are used to represent valuation operators in dynamic stochastic economies. A kernel is commonlyused mathematical term used to represent an operator. The term stochastic discount factor extends concepts from economics and finance to include adjustments for risk. As we will see, there is a tight connection between t...

An all-units discount is a price reduction applied to all units purchased if the customer’s total purchases equal or exceed a given quantity threshold. Since the discount is paid on all units rather than marginal units, the tariff is discontinuous and exhibits a negative marginal price (“cliff”) at the threshold that triggers the discount. This paper shows that all-units discounts arise in opti...

This paper develops and studies a tough love model of intergenerational altruism. We model tough love by modifying the Barro-Becker standard altruism model in two ways. First, the child’s discount factor is endogenously determined, so that low consumption at young age leads to a higher discount factor later in her life. Second, the parent evaluates the child’s lifetime utility with a constant h...

In contrast to the existing literature on repeated games that assumes a Þxed discount factor, I study an environment in which it is more realistic to assume a ßuctuating discount factor. In a repeated oligopoly, as the interest rate changes, so too does the degree to which Þrms discount the future. I characterize the optimal tacit collusion equilibrium when the discount factor changes over time...

For general state and action space Markov decision processes, we present sufficient conditions for convergence of both the optimal discounted cost value function and policies to the corresponding objects for the average costs per unit time. We extend Schäl’s [24] assumptions, guaranteeing the existence of a solution to the average cost optimality inequalities for compact action sets, to non-com...