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Pricing under noisy signaling

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Abstract

We provide rationale, conditions, and insights for “customized” pricing in markets, that is, for equilibria where different buyers pay different prices for similar products. We use a Spence/Riley signaling model enhanced by a signaling methodology under random relations between costs and attributes, developed by Feldman (Math Soc Sci 48:93–101, 2004) and Feldman and Winer (Math Soc Sci 48:81–91, 2004). Examples include markets for new cars, retail, human capital, trades where transaction costs are negotiable, and transactions where sellers affect buyers’ costs by offering different levels of service or support for the same products and prices. These encompass a large fraction of all assets, prices, and transactions. Our results help explain the different levels of segmentation and product/service differentiation that we observe in markets and the efficiency of these equilibria. We note that we can demonstrate the results within competitive sellers’ markets. Financial markets examples include dividend, initial public offerings, market microstructure and capital structure signaling, and share class distinctions in mutual funds.

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Notes

  1. Throughout the paper, we use the term “separating” to mean fully separating. This paper’s results, however, hold for partially separating equilibria as well. When the appropriate boundary conditions hold, we have full separation.

  2. See Lehmann (1959) for definitions and use of the MLRP in probability and statistics, and Milgrom (1981) for its role in information economics.

  3. The GMLRP, defined by FW, can order probability distributions induced by probability distributions. The MLRP orders probability distributions induced by realizations only.

  4. We interpret “level of information” as one dimensional measure of both quality and quantity of information.

  5. The case where θ l  = θ h is economically redundant, thus excluded.

  6. For simplicity and brevity, we assume a binary attribute. Our results hold for multiple possible attribute values.

  7. We choose the simpler notation f(c) over more elaborate ones, such as \(f_{c|\theta } (c|\theta_{i} )\), and even \(f(c|\theta_{i} ).\)

  8. Our analysis stands if buyers observe their costs but not their attributes.

  9. As said earlier, buyers’ attributes could be unobservable to buyers as well.

  10. Without loss of generality, for simplicity, we assume positive signals.

  11. To simplify the exposition and notation, we assume a linear signaling cost structure where the signaling cost is sc. Our results hold for a general signaling cost function C(s, c) under appropriate assumptions about the function’s partial derivatives.

  12. See Lehmann (1959) for the definition of MLRP, and see Milgrom (1981) for an examination of the informational role of the MLRP.

  13. After multiplying both sides of inequality (15) by c.

  14. See Milgrom (1981, Proposition 2).

  15. See, F and, for example, Lehmann (1959, p. 74).

  16. For notational brevity, we suppress the subscripts of the probability distribution functions. The arguments will define the functions, i.e., \(f(c|\theta ) \triangleq f_{c|\theta } (c|\theta )\), etc.

  17. As before, in the previous subsection, to simplify exposition and notation, we assume a linear signaling cost structure where the signaling cost is sc. Our results hold for a general signaling cost function C(s, c) under appropriate assumptions about the function’s partial derivatives.

  18. To simplify the exposition, we assume mathematical conditions for separation by cost that are more restricting than necessary. For example, we can allow b′(c) = 0 for some c.

  19. These are the necessary and sufficient conditions for buyers’ cost minimization under the cost structure specified in Eq. (18). Different cost structures would induce corresponding conditions.

  20. After multiplying both sides of inequality (15) by c.

  21. See, F and, for example, Lehmann (1959, p. 74).

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Acknowledgments

We thank Linda Pesante, participants of The Annual Conference on Pacific Basin Finance, Economics, Accounting, and Management, The Econometric Society European Meetings, The Australasian Finance and Banking Conference, and seminar participants at The University of New South Wales, The University of Melbourne, and The University of Western Australia.

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Authors and Affiliations

  1. Banking and Finance, The Australian School of Business, University of New South Wales, UNSW Sydney, NSW, 2052, Australia

    David Feldman

  2. Kelley School of Business, Indiana University, 1309 East Tenth Street, Bloomington, IN, 47405-1701, USA

    Charles Trzcinka

  3. Stern School of Business, New York University, 44 West 4th Street, New York, NY, 10012, USA

    Russell S. Winer

Authors
  1. David Feldman
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  2. Charles Trzcinka
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  3. Russell S. Winer
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Correspondence to David Feldman.

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Feldman, D., Trzcinka, C. & Winer, R.S. Pricing under noisy signaling. Rev Quant Finan Acc 45, 435–454 (2015). https://doi.org/10.1007/s11156-014-0442-8

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