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Repeated Trade With Imperfect Information About Previous Transactions

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  • Francesc Dilmé

Abstract

This paper studies repeated trade with noisy information about previous transactions. A buyer has private information about his willingness to pay, which is either low or high, and buys goods from different sellers over time. Each seller observes a noisy history of signals about the buyer’s previous purchases and sets a price. We compare the cases where previous prices are observable to sellers with the case where they are not. We show that more signal precision is counterbalanced by two equilibrium mechanisms that slow learning and keep incentives in balance: (1) sellers offer discounted prices more often, and (2) the buyer rejects high prices with a higher probability. The effect of making prices observable depends on the signal precision: When the signal is imprecise, making prices public strengthens the discounting mechanism, improving efficiency and buyer welfare; when the signal is precise, making prices public activates the rejection mechanism, and efficiency and buyer welfare may decrease. Independently of the price observability, the buyer tends to benefit from a more precise signal about previous purchases.

Suggested Citation

  • Francesc Dilmé, 2024. "Repeated Trade With Imperfect Information About Previous Transactions," CRC TR 224 Discussion Paper Series crctr224_2024_538, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2024_538
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp538
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    References listed on IDEAS

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    1. Garrett A. Johnson & Scott K. Shriver & Shaoyin Du, 2020. "Consumer Privacy Choice in Online Advertising: Who Opts Out and at What Cost to Industry?," Marketing Science, INFORMS, vol. 39(1), pages 33-51, January.
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    Keywords

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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