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Terminal Ranking Games

Author

Listed:
  • Erhan Bayraktar

    (Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104)

  • Yuchong Zhang

    (Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5G 1Z5, Canada)

Abstract

We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schrödinger bridges we are able to explicitly calculate the equilibrium. This allows us to identify the reward functions which would yield a desired equilibrium and solve several related mechanism design problems. We are also able to identify the effect of reward inequality on the players’ welfare as well as calculate the price of anarchy.

Suggested Citation

  • Erhan Bayraktar & Yuchong Zhang, 2021. "Terminal Ranking Games," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1349-1365, November.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:4:p:1349-1365
    DOI: 10.1287/moor.2020.1107
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