liability, R = R(Q). Consumers choose how much reliability they want and pay in advance based on the payment schedule. Consumer i chooses reliability to maximize net benefits: The consumer chooses a level of reliability Qi* that equates the marginal payment for reliability to the consumer's willingness to pay for a unit of service: bi=='R'(Qi*). It can be shown that given an optimal payment schedule, consumers with a greater willingness to pay for a unit of service choose a higher level of reliability. The reliability payment schedule must be increasing in reliability. Thus, consumers with a greater willingness to pay for a unit of service choose to pay more for reliability of service. Suppose that consumer willingness-to-pay levels are arranged in increasing order, b'<b2<...<bl. Then the consumers with the K highest willingness-to-pay levels each receive a unit of service. Thus, the outcome of the allocation process with a reliability payment schedule corresponds exactly to the allocation in the Vickrey auction. We examine how the reliability and payment schedules compare to the Vickrey auction. We present an intuitive approach to the design of an optimal reliability payment schedule. First, define the consumer's virtual marginal willingness to pay for capacity by subtracting (1- - F(b)))/f(bi) from the consumer's willingness to pay, bi Pricing Network Services This is the exact amount by which consumers understate their willingness to pay under asymmetric information.6 Thus, define the consumer's virtual demand function by otherwise. The virtual demand function of consumer idepends on the shadow price of capacity p and the individual's value of a unit of service, which equals bi. Now, calculate the sum of virtual demands to obtain aggregate virtual demand, Then use the aggregate virtual demand to calculate the shadow price of capacity, p*, which clears the market, Clearly, the shadow price of capacity will depend on all of the consumer val- uations of service: p*=p* (b1, b2,..., b1, K). The shadow price also de