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Values for two-stage games: Another view of the Shapley axioms

Author

Listed:
  • Itzhak Gilboa

    (Northwestern University [Evanston])

  • A. Beja

    (TAU - Tel Aviv University, MIT - Massachusetts Institute of Technology)

Abstract

This short study reports an application of the Shapley value axioms to a new concept of ldquotwo-stage games.rdquo In these games, the formation of a coalition in the first stage entitles its members to play a prespecified cooperative game at the second stage. The original Shapley axioms have natural equivalents in the new framework, and we show the existence of (non-unique) values and semivalues for two stage games, analogous to those defined by the corresponding axioms for the conventional (one-stage) games. However, we also prove that all semivalues (hence, perforce, all values) must give patently unacceptable solutions for some ldquotwo-stage majority gamesrdquo (where the members of a majority coalition play a conventional majority game). Our reservations about these prescribed values are related to Roth's (1980) criticism of Shapley's ldquolambda-transfer valuerdquo for non-transferable utility (NTU) games. But our analysis has wider scope than Roth's example, and the argument that it offers appears to be more conclusive. The study also indicates how the values and semivalues for two-stage games can be naturally generalized to apply for ldquomulti-stage games.rdquo

Suggested Citation

  • Itzhak Gilboa & A. Beja, 1990. "Values for two-stage games: Another view of the Shapley axioms," Post-Print hal-00481652, HAL.
    • Handle: RePEc:hal:journl:hal-00481652
    DOI: 10.1007/BF01753705
    as

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    Cited by:

    1. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, October.
    2. Gilboa, Itzhak & Lehrer, Ehud, 1991. "Global Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 129-147.

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