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Analyzing Scrip Systems

Author

Listed:
  • Kris Johnson

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • David Simchi-Levi

    (Engineering Systems Division, Department of Civil and Environmental Engineering, and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Peng Sun

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

Scrip systems provide a nonmonetary trade economy for exchange of resources. We model a scrip system as a stochastic game and study system design issues on selection rules to match potential trade partners over time. We show the optimality of one particular rule in terms of maximizing social welfare for a given scrip system that guarantees players' incentives to participate. We also investigate the optimal number of scrips to issue under this rule. In particular, if the time discount factor is close enough to one, or trade benefits one partner much more than it costs the other, the maximum social welfare is always achieved no matter how many scrips are in the system. When the benefit of trade and time discount are not sufficiently large, on the other hand, injecting more scrips in the system hurts most participants; as a result, there is an upper bound on the number of scrips allowed in the system, above which some players may default. We show that this upper bound increases with the discount factor as well as the ratio between the benefit and cost of service. Finally, we demonstrate similar properties for a different service provider selection rule that has been analyzed in previous literature.

Suggested Citation

  • Kris Johnson & David Simchi-Levi & Peng Sun, 2014. "Analyzing Scrip Systems," Operations Research, INFORMS, vol. 62(3), pages 524-534, June.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:3:p:524-534
    DOI: 10.1287/opre.2014.1260
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    References listed on IDEAS

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    1. Thorsten Hens & Klaus Reiner Schenk‐Hoppé & Bodo Vogt, 2007. "The Great Capitol Hill Baby Sitting Co‐op: Anecdote or Evidence for the Optimum Quantity of Money?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1305-1333, September.
    2. Sweeney, Joan & Sweeney, Richard James, 1977. "Monetary Theory and the Great Capitol Hill Baby Sitting Co-op Crisis: Comment," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 9(1), pages 86-89, February.
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    Cited by:

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    8. Shivam Gupta & Wei Chen & Milind Dawande & Ganesh Janakiraman, 2023. "Three Years, Two Papers, One Course Off: Optimal Nonmonetary Reward Policies," Management Science, INFORMS, vol. 69(5), pages 2852-2869, May.
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    10. Ezzat Elokda & Saverio Bolognani & Andrea Censi & Florian Dörfler & Emilio Frazzoli, 2024. "A Self-Contained Karma Economy for the Dynamic Allocation of Common Resources," Dynamic Games and Applications, Springer, vol. 14(3), pages 578-610, July.

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