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Bystanders

Author

Listed:
  • Amihai Glazer

    (University of California, Irvine)

  • Refael Hassin

    (Tel Aviv University)

  • Irit Nowik

    (Jerusalem College of Technology)

Abstract

The standard bystander problem appears when the costly action of one person benefits many others. Two problems can appear: a free-rider problem with each person preferring that others incur the cost, and a coordination problem where more than one person may incur the cost, which is wasteful. We extend the standard model in several ways. We consider a random number of people who may act, rather than only a fixed number, and with some people who are unable to act benefiting from someone else’s action. The equilibrium probability that a person acts is larger with a random number than with a fixed number. Despite that, the probability that at least one person acts and the values of welfare in equilibrium and at the social optimum, are greater when the number of people who can act is fixed than when it is random. We consider three reward mechanisms to induce efficient behavior. The gain from inducing a welfare-maximizing solution can be large: with a large group size, the benefit increases by the cost of acting. Lastly, we have the authority sometimes not respond to a report, and analyze the implications when the response is costless or costly.

Suggested Citation

  • Amihai Glazer & Refael Hassin & Irit Nowik, 2025. "Bystanders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 65(1), pages 211-253, August.
    • Handle: RePEc:spr:sochwe:v:65:y:2025:i:1:d:10.1007_s00355-024-01570-x
    DOI: 10.1007/s00355-024-01570-x
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