We study optimal nonuniform pricing in a setting where a customer's demand at the start of a billing period contains a random variable whose realization becomes known by the end of the billing period. In this context, an optional calling plan is a tariff which the consumer must select based on his/her expectations about the random variable, whereas, under a tapered tariff, the consumer's choice of usage charge is made after he/she knows the realization of the random variable. We show that for low to moderate levels of uncertainty about the random variable entering the demand function, the optional calling plan approach to nonuniform pricing yields higher expected profit than does the tapered tariff approach, given risk-neutral consumers. We illustrate this finding with a case study and argue that it is consistent with the historical evolution of tariffs in the interexchange telecommunications market.

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We study a principal-agent game where the principal commits to an a#ne contract. We suppose that the principal has incomplete information but he can adjust the contract according to the myopically behaving agent's reactions when the game is played repeatedly. The adjustment process can be considered as a learning model. We derive convergence conditions for fixed-point iteration as an adjustment scheme and study a related continuous time process. The analysis is based on parameterizing the problem such that we obtain a degree zero homogeneous system of equations, where the nonlinear mapping satisfies Walras' law.

Physically constrained subscription-based telephone network services can experience opposing market forces which affect new product adoption. In such networks, a positive externality due to increases in subscribership encourages more consumers to sign up. As a result, the addition of users to the system then leads to an increase in network load (measured in call minutes for the entire system). At some point, call demand exceeds network capacity and subscribers are forced to wait for call completion. This translates to a negative externality in the form of congestion and not only reduces the consumption by current customers but also discourages subscriber set expansion. These concurrent positive and negative externalities ultimately determine demand dynamics, given subscriber attitudes and pricing changes. A typical example of these subscription-based services can be found in the mobile communications industry. In the past few years, metropolitan cellular telephone has been plagued by m...

We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multi-dimensional preferences over several possible configurations of the good (furthermore, it allows an agent’s budget and risk preference to be known only privately to the agent). These are the main challenge areas for auction theory. A single-agent problem is to optimize a given objective subject to a constraint on the maximum probability with which each type is allocated, a.k.a., an allocation rule. Our approach is a reduction from multi-agent mechanism design problem to collection of single-agent problems. We focus on maximizing revenue, but our results can be applied to other objectives (e.g., welfare). An optimal multi-agent mechanism can be computed by a linear/convex program on interim allocation rules by simultaneously optimizing several single-agent mechanisms subject to joint feasibility of the allocation rules. For single-unit auctions, Border (1991) showed that the space of all jointly feasible interim allocation rules for n agents is a D-dimensional convex polytope which can be specified by 2D linear constraints, where D is the total number of all agents’