IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v6y2016i4d10.1007_s13235-015-0158-y.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-015-0158-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-015-0158-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    4. 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.
    5. 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.
    6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    7. Ted Klastorin & Weiyu Tsai, 2004. "New Product Introduction: Timing, Design, and Pricing," Manufacturing & Service Operations Management, INFORMS, vol. 6(4), pages 302-320, August.
    8. 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.
    9. Liran Einav, 2007. "Seasonality in the U.S. motion picture industry," RAND Journal of Economics, RAND Corporation, vol. 38(1), pages 127-145, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Platz, Trine Tornøe & Østerdal, Lars Peter, 2017. "The curse of the first-in–first-out queue discipline," Games and Economic Behavior, Elsevier, vol. 104(C), pages 165-176.
    2. Breinbjerg, Jesper, 2017. "Equilibrium arrival times to queues with general service times and non-linear utility functions," European Journal of Operational Research, Elsevier, vol. 261(2), pages 595-605.
    3. Breinbjerg, Jesper & Østerdal, Lars Peter, 2017. "Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume," Discussion Papers on Economics 3/2017, University of Southern Denmark, Department of Economics.
    4. 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.
    5. Jesper Breinbjerg & Trine Tornøe Platz & Lars Peter Østerdal, 2024. "Equilibrium arrivals to a last-come first-served preemptive-resume queue," Annals of Operations Research, Springer, vol. 336(3), pages 1551-1572, May.
    6. Jesper Breinbjerg & Alexander Sebald & Lars Peter Østerdal, 2016. "Strategic behavior and social outcomes in a bottleneck queue: experimental evidence," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 207-236, September.
    7. Moshe Haviv & Liron Ravner, 2014. "Strategic timing of arrivals to a finite queue multi-server loss system," Discussion Paper Series dp675, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    8. Sakuma, Yutaka & Masuyama, Hiroyuki & Fukuda, Emiko, 2020. "A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 253-264.
    9. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    10. Breinbjerg, Jesper, 2016. "Strategic Arrival Times to Queueing Systems," Discussion Papers on Economics 6/2016, University of Southern Denmark, Department of Economics.
    11. William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 885-915.
    12. Bobtcheff, Catherine & Mariotti, Thomas, 2012. "Potential competition in preemption games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 53-66.
    13. Sandeep Juneja, 2022. "Learning the queue arrivals game equilibrium," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 533-535, April.
    14. Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
    15. Ravner, Liron & Haviv, Moshe & Vu, Hai L., 2016. "A strategic timing of arrivals to a linear slowdown processor sharing system," European Journal of Operational Research, Elsevier, vol. 255(2), pages 496-504.
    16. de Palma, André & Fosgerau, Mogens, 2013. "Random queues and risk averse users," European Journal of Operational Research, Elsevier, vol. 230(2), pages 313-320.
    17. Liron Ravner & Yutaka Sakuma, 2021. "Strategic arrivals to a queue with service rate uncertainty," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 303-341, April.
    18. Ghosh, Souvik & Hassin, Refael, 2021. "Inefficiency in stochastic queueing systems with strategic customers," European Journal of Operational Research, Elsevier, vol. 295(1), pages 1-11.
    19. Alon, Tzvi & Haviv, Moshe, 2022. "Discrete-time strategic job arrivals to a single machine with waiting and lateness penalties," European Journal of Operational Research, Elsevier, vol. 303(1), pages 480-486.
    20. Kerstan, Sven & Kretschmer, Tobias & Muehlfeld, Katrin, 2012. "The dynamics of pre-market standardization," Information Economics and Policy, Elsevier, vol. 24(2), pages 105-119.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:dyngam:v:6:y:2016:i:4:d:10.1007_s13235-015-0158-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.