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The Reactive Bargaining Set: Structure, Dynamics and Extension to NTU Games

Author

Listed:
  • Daniel Granot

    (Faculty of Commerce and Business Administration, The University of British Columbia, 2053 Main Mall, Vancouver, B.C. Canada V6T 1Z2)

  • Michael Maschler

    (The Hebrew University of Jerusalem, Israel)

Abstract

The reactive bargaining set (Granot [1994]) is the set of outcomes for which no justified objection exists. Here, in a justified objection the objector first watches how the target tries to act (if he has such an option), and then reacts by making a profit and ruining the target's attempt to maintain his share. In this paper we explore properties of the reactive bargaining set, set up the system of inequalities that defines it, and construct a dynamic system in the sense of Stearns' transfer scheme that leads the players to this set. We also extend the definition of the reactive bargaining set to NTU games in a way that keeps it nonempty. To shed light on its nature and its relative ease of computation, we compute the reactive bargaining set for games that played important role in the game theory literature.

Suggested Citation

  • Daniel Granot & Michael Maschler, 1997. "The Reactive Bargaining Set: Structure, Dynamics and Extension to NTU Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 75-95.
    • Handle: RePEc:spr:jogath:v:26:y:1997:i:1:p:75-95
    Note: Received January 1995 Revised version August 1995
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    Cited by:

    1. Massimo Morelli & Maria Montero, 2001. "The Stable Demand Set General Characterization and Application to Majority Games," Working Papers 01-03, Ohio State University, Department of Economics.
    2. Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.
    3. Morelli, Massimo & Montero, Maria, 2003. "The demand bargaining set: general characterization and application to majority games," Games and Economic Behavior, Elsevier, vol. 42(1), pages 137-155, January.

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