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The Ordered Timeline Game: Strategic Posting Times Over a Temporally Ordered Shared Medium

Author

Listed:
  • Eitan Altman

    (INRIA)

  • Nahum Shimkin

    (Technion—Israel Institute of Technology)

Abstract

We consider a game of timing between a random number of content creators, who compete for position and exposure time over an ordered shared medium such as an online classified list. Contents (such as ads, messages, multimedia items, or comments) are ordered according to their submission times, with more recent submissions displayed at the top (and better) positions. The instantaneous effectiveness of each item depends on its current display position, as well as on a time-dependent site exposure function which is common to all. Each content creator may choose the submission time of his or her item within a finite time interval, with the goal of maximizing the total exposure of this item. We formulate the problem as a noncooperative game and analyze its symmetric Nash equilibrium. We show existence of the equilibrium profile, characterize it in terms of a differential boundary value problem, provide sufficient conditions for its uniqueness, and devise a numerical scheme for its computation. We further compute the equilibrium profile explicitly for certain special cases, which include a two-player small match and a Poisson-distributed number of players, and evaluate the social efficiency of these equilibria.

Suggested Citation

  • Eitan Altman & Nahum Shimkin, 2016. "The Ordered Timeline Game: Strategic Posting Times Over a Temporally Ordered Shared Medium," Dynamic Games and Applications, Springer, vol. 6(4), pages 429-455, December.
    • Handle: RePEc:spr:dyngam:v:6:y:2016:i:4:d:10.1007_s13235-015-0158-y
    DOI: 10.1007/s13235-015-0158-y
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    References listed on IDEAS

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    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    2. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    3. Rajagopal, 2007. "New Product Introduction and Seasonality Effect in Food Products Retailing," Marketing Working Papers 2007-01-MKT, Tecnológico de Monterrey, Campus Ciudad de México.
    4. Glazer, Amihai & Hassin, Refael, 1983. "?/M/1: On the equilibrium distribution of customer arrivals," European Journal of Operational Research, Elsevier, vol. 13(2), pages 146-150, June.
    5. Lotker, Zvi & Patt-Shamir, Boaz & Tuttle, Mark R., 2008. "A game of timing and visibility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 643-660, March.
    6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    7. Refael Hassin & Yana Kleiner, 2011. "Equilibrium and optimal arrival patterns to a server with opening and closing times," IISE Transactions, Taylor & Francis Journals, vol. 43(3), pages 164-175.
    8. Liran Einav, 2007. "Seasonality in the U.S. motion picture industry," RAND Journal of Economics, RAND Corporation, vol. 38(1), pages 127-145, March.
    9. Ted Klastorin & Weiyu Tsai, 2004. "New Product Introduction: Timing, Design, and Pricing," Manufacturing & Service Operations Management, INFORMS, vol. 6(4), pages 302-320, August.
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    Cited by:

    1. Moshe Haviv & Liron Ravner, 2021. "A survey of queueing systems with strategic timing of arrivals," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 163-198, October.

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