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Evolutionary stability in the generalized second-price auction

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  • Thomas W. L. Norman

    (Magdalen College)

Abstract

The “generalized second-price auction” is widely employed to sell internet advertising positions and has many equilibria. Analysis of this auction has assumed that myopic players commonly know each others’ position values, and that the resulting equilibrium play is “locally envy-free”. Here, I argue that the appropriate refinement of Nash equilibrium for this setting is evolutionary stability, and show that it implies that an equilibrium is locally envy-free if the whole population of players bids in each auction and the set of possible bids is not too coarse. However, not all locally envy-free equilibria are evolutionarily stable in this case, as I show by example for the popular Vickrey–Clarke–Groves outcome. The existence of evolutionarily stable equilibrium is established when one position is auctioned, as well as for two positions and a large number of bidders.

Suggested Citation

  • Thomas W. L. Norman, 2021. "Evolutionary stability in the generalized second-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 235-250, February.
    • Handle: RePEc:spr:joecth:v:71:y:2021:i:1:d:10.1007_s00199-019-01240-5
    DOI: 10.1007/s00199-019-01240-5
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    Cited by:

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    2. Margarida V. B. Santos & Isabel Mota & Pedro Campos, 2023. "Analysis of online position auctions for search engine marketing," Journal of Marketing Analytics, Palgrave Macmillan, vol. 11(3), pages 409-425, September.
    3. Gino Loyola, 2021. "Effects of competition in first-price auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1527-1567, June.

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    More about this item

    Keywords

    Online advertising; Internet auctions; Position auctions; Evolutionarily stable strategy; Locally envy-free equilibrium; Symmetric Nash equilibrium; Vickrey–Clarke–Groves outcome; Spite;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L81 - Industrial Organization - - Industry Studies: Services - - - Retail and Wholesale Trade; e-Commerce
    • L86 - Industrial Organization - - Industry Studies: Services - - - Information and Internet Services; Computer Software
    • M3 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising

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