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The effect of choosing a proposer through a bidding procedure in implementing the Shapley value

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  • Michela Chessa
  • Nobuyuki Hanaki
  • Aymeric Lardon
  • Takashi Yamada

Abstract

We experimentally compare a simplified version of two mechanisms that implement the Shapley value as an (ex ante) equilibrium outcome of a noncooperative bargaining procedure: one proposed by Hart and Mas-Colell (1996, H-MC) and the other by Perez-Castrillo and Wettstein (2001, PC-W). While H-MC induces the Shapley value only on average, PC-W does so as a unique equilibrium outcome by introducing an additional bidding stage on top of H-MC. We investigate the effect of this additional bidding stage on the resulting outcomes such as the frequency of grand coalition formation, efficiency, and the distance between the realized allocation and the Shapley value. Our experiment shows that H-MC not only results in significantly greater efficiency than PC-W, but also that the average allocation is closer to the Shapley value for those groups that formed the grand coalition. This difference is because those proposers who won the bidding stage in PC-W tend to offer an allocation that favors themselves more than the randomly chosen proposers in H-MC, and such offers are more likely to be rejected.

Suggested Citation

  • Michela Chessa & Nobuyuki Hanaki & Aymeric Lardon & Takashi Yamada, 2022. "The effect of choosing a proposer through a bidding procedure in implementing the Shapley value," ISER Discussion Paper 1176r, Institute of Social and Economic Research, Osaka University, revised Aug 2022.
    • Handle: RePEc:dpr:wpaper:1176r
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    References listed on IDEAS

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

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