Solution Structures in Non-ordered Discrete Screening Problems: Trees, Stars and Cycles

Nahata, Babu; Kokovin, Sergey; Zhelobodko, Evegeny

doi:10.2139/ssrn.909293

Cited by 3 publications

(13 citation statements)

References 14 publications

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“…, n}. The buyers are assumed to be friendly (Nahata et al 2004), i.e., they choose the most profitable bundle for the firm when they are indifferent between two or more bundles. The firm's problem can now be formulated as…”

Section: Nonlinear Pricing Modelmentioning

confidence: 99%

“…The second assumption is that there is only one quality dimension and the single-crossing assumption is satisfied. With more buyer types and multiple dimensions, there are more possible solution structures and finding the optimal structure is more complicated Ehtamo 2008, 2009;Nahata et al 2004).…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…This means that (a) is no longer possible, and the optimum must be of characteristic (b); this structure is more generally known as chain (Nahata et al 2004). We also assume that q * L > 0 and the second-order condition )…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…The multidimensional pricing problem has been studied by Wilson (1993), Armstrong (1996), Rochet and Chone (1998), Nahata et al (2002) and Basov (2005). See also Armstrong (2006) and Stole (2007) for recent surveys on price discrimination.…”

Section: Introductionmentioning

confidence: 99%

“…Many papers on pricing assume so-called single-crossing condition, which restricts the shape of buyers' possible utility functions. There are, however, few papers that examine a model without it (e.g., Araujo and Moreira 1999;Nahata et al 2004;Berg and Ehtamo 2008). In this paper we assume the single-crossing condition to illustrate the learning idea better and the learning methods can be applied in the more general model as well.…”

Section: Introductionmentioning

confidence: 99%

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Continuous learning methods in two-buyer pricing problem

Berg

Ehtamo

2012

Math Meth Oper Res

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This paper presents continuous learning methods in a monopoly pricing problem where the firm has uncertainty about the buyers' preferences. The firm designs a menu of quality-price bundles and adjusts them using only local information about the buyers' preferences. The learning methods define different paths, and we compare how much profit the firm makes on these paths, how long it takes to learn the optimal tariff, and how the buyers' utilities change during the learning period. We also present a way to compute the optimal path in terms of discounted profit with dynamic programming and complete information. Numerical examples show that the optimal path may involve jumps where the buyer types switch from one bundle to another, and this is a property which is difficult to include in the learning methods. The learning methods have, however, the benefit that they can be generalized to pricing problems with many buyers types and qualities.

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Section: Nonlinear Pricing Modelmentioning

confidence: 99%

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Continuous learning methods in two-buyer pricing problem

Berg

Ehtamo

2012

Math Meth Oper Res

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Complexity of solution structures in nonlinear pricing

Berg

2013

Ann Oper Res

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Multidimensional screening

Berg¹,

Ehtamo²

2008

Proceedings of the 10th International Conference on Electronic Commerce

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Optimal screening has been studied in economics, game theory, and recently computer science. We study the problem in a nonlinear pricing application, where a monopoly designs a price schedule from which the buyers self-select the quality they wish to consume. We formulate a multidimensional model with buyers' utility functions that need not satisfy the standard single-crossing assumption. We characterize the solution with the first-order optimality conditions and present a framework for analyzing the solution. With the framework, the structure of the solution is easily illustrated and the sensitivity analysis can be done. We give numerical examples that demonstrate the properties of the solution. With these observations, we discuss the complexity of the problem and solving the problem under limited information. We examine what information the monopoly needs when adjusting the price schedule to increase the profit. This paper applies, e.g., to pricing situations in electronic commerce where the seller may have limited information available, and the seller learns about the buyers' preferences online when doing the business.

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Solution Structures in Non-ordered Discrete Screening Problems: Trees, Stars and Cycles

Cited by 3 publications

References 14 publications

Continuous learning methods in two-buyer pricing problem

Continuous learning methods in two-buyer pricing problem

Complexity of solution structures in nonlinear pricing

Multidimensional screening

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