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Batch Queues with Choice of Arrivals: Equilibrium Analysis and Experimental Study


  • William E. Stein

    (Texas A&M University)

  • Amnon Rapoport

    (University of Arizona & Hong Kong University of Science & Technology)

  • Darryl A. Seale

    (University of Nevada Las Vegas)

  • Hongtao Zhang

    (Hong Kong University of Science & Technology)

  • Rami Zwick

    (Hong Kong University of Science & Technology)


We study both theoretically and experimentally the decisions players make in two queueing games with batch service. In both games, players are asked to independently decide when to join a discrete-time queue to receive service, or they may simply choose not to join it at all. Equilibrium solutions in pure and mixed strategies are constructed for two games where balking is prohibited and where it is allowed. They are then tested experimentally in a study that varies the game type (balking vs. no balking) and information structure (private vs. public information) in a 2X2 between-subject design. With repeated iterations of the stage game, all four experimental conditions result in aggregate, but not individual, behavior approaching mixed-strategy equilibrium play.

Suggested Citation

  • William E. Stein & Amnon Rapoport & Darryl A. Seale & Hongtao Zhang & Rami Zwick, 2004. "Batch Queues with Choice of Arrivals: Equilibrium Analysis and Experimental Study," Experimental 0411001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpex:0411001
    Note: Type of Document - pdf; pages: 45

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    References listed on IDEAS

    1. Ockenfels, Axel & Selten, Reinhard, 2005. "Impulse balance equilibrium and feedback in first price auctions," Games and Economic Behavior, Elsevier, vol. 51(1), pages 155-170, April.
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    3. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    4. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    5. Howard J. Weiss, 1979. "The Computation of Optimal Control Limits for a Queue with Batch Services," Management Science, INFORMS, vol. 25(4), pages 320-328, April.
    6. Darryl Seale & James Parco & William Stein & Amnon Rapoport, 2005. "Joining a Queue or Staying Out: Effects of Information Structure and Service Time on Arrival and Staying Out Decisions," Experimental Economics, Springer;Economic Science Association, vol. 8(2), pages 117-144, June.
    7. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    8. Rapoport, Amnon & Seale, Darryl A. & Winter, Eyal, 2002. "Coordination and Learning Behavior in Large Groups with Asymmetric Players," Games and Economic Behavior, Elsevier, vol. 39(1), pages 111-136, April.
    9. Holt, Charles A, Jr & Sherman, Roger, 1982. "Waiting-Line Auctions," Journal of Political Economy, University of Chicago Press, vol. 90(2), pages 280-294, April.
    10. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
    11. Rapoport, Amnon & Stein, William E. & Parco, James E. & Seale, Darryl A., 2004. "Equilibrium play in single-server queues with endogenously determined arrival times," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 67-91, September.
    12. J. Medhi, 1975. "Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule," Management Science, INFORMS, vol. 21(7), pages 777-782, March.
    13. Darryl Seale & Amnon Rapoport, 2000. "Elicitation of Strategy Profiles in Large Group Coordination Games," Experimental Economics, Springer;Economic Science Association, vol. 3(2), pages 153-179, October.
    14. Eyal Winter & Amnon Rapoport & Darryl A. Seale, 2000. "An experimental study of coordination and learning in iterated two-market entry games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(3), pages 661-687.
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    Cited by:

    1. Anna Conte & Marco Scarsini & Oktay Sürücü, 2016. "The impact of time limitation: Insights from a queueing experiment," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 11(3), pages 260-274, May.
    2. Rapoport, Amnon & Stein, William E. & Mak, Vincent & Zwick, Rami & Seale, Darryl A., 2010. "Endogenous arrivals in batch queues with constant or variable capacity," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1166-1185, December.
    3. Breinbjerg, Jesper & Østerdal, Lars Peter, 2017. "Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume," Discussion Papers of Business and Economics 3/2017, University of Southern Denmark, Department of Business and Economics.
    4. 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.
    5. Conte, Anna & Scarsini, Marco & Sürücü, Oktay, 2015. "Does time pressure impair performance? An experiment on queueing behavior," Center for Mathematical Economics Working Papers 538, Center for Mathematical Economics, Bielefeld University.
    6. Anouar El Haji & Sander Onderstal, 2015. "Trading Places: An Experimental Comparison of Reallocation Mechanisms for Priority Queuing," Tinbergen Institute Discussion Papers 15-063/VII, Tinbergen Institute.
    7. Ziani, Sofiane & Rahmoune, Fazia & Radjef, Mohammed Said, 2015. "Customers’ strategic behavior in batch arrivals M2/M/1 queue," European Journal of Operational Research, Elsevier, vol. 247(3), pages 895-903.
    8. Sun, Li & Liu, Like & Xu, Zhongzhi & Jie, Yang & Wei, Dong & Wang, Pu, 2015. "Locating inefficient links in a large-scale transportation network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 537-545.
    9. Delgado-Alvarez, Carlos A. & van Ackere, Ann & Larsen, Erik R & Arango-Aramburo, Santiago, 2017. "Managing capacity at a service facility: An experimental approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 216-228.
    10. Breinbjerg, Jesper, 2016. "Strategic Arrival Times to Queueing Systems," Discussion Papers of Business and Economics 6/2016, University of Southern Denmark, Department of Business and Economics.
    11. repec:eee:ejores:v:261:y:2017:i:2:p:595-605 is not listed on IDEAS
    12. Otsubo, Hironori & Rapoport, Amnon, 2008. "Vickrey's model of traffic congestion discretized," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 873-889, December.

    More about this item


    Batch queueing; equilibrium solution; experimental economics;

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General

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