A non-cooperative interpretation of bargaining sets

Abstract. This paper provides a non-cooperative interpretation for bargaining sets concepts in economic environments. We investigate the implementability of the Aumann-Maschler and Mas-Colell bargaining sets, and provide mechanisms whose subgame perfect equilibrium outcomes realize these sets. These mechanisms, in contrast to general mechanisms suggested in the implementation literature, have a natural structure closely related to that of the rationale underlying the bargaining sets. Furthermore, the strategy sets consist mainly of allocations and coalitions (thus avoiding any reference to preference parameters) and are finite dimensional.

[1]  P. Reny,et al.  A Noncooperative View of Coalition Formation and the Core , 1994 .

[2]  Hitoshi Matsushima,et al.  Virtual implementation in iteratively undominated strategies: complete information , 1992 .

[3]  M. Jackson.  Implementation in Undominated Strategies: A Look at Bounded Mechanisms , 1992 .

[4]  Roberto Serrano.  Non-cooperative implementation of the nucleolus: The 3-player case , 1993 .

[5]  S. Hart,et al.  Bargaining and Value , 1996 .

[6]  Two Characterizations of Bargaining Sets , 1992 .

[7]  R. Aumann,et al.  THE BARGAINING SET FOR COOPERATIVE GAMES , 1961 .

[8]  Hitoshi Matsushima.  A new approach to the implementation problem , 1988 .

[9]  Faruk Gul.  Bargaining Foundations of Shapley Value , 1989 .

[10]  David Wettstein,et al.  Implementation of Bargaining Sets via Simple Mechanisms , 2000, Games Econ. Behav..

[11]  Debraj Ray,et al.  A consistent bargaining set , 1989 .

[12]  A. Mas-Colell.  An equivalence theorem for a bargaining set , 1989 .

[13]  Roberto Serrano,et al.  A Market to Implement the Core , 1995 .

[14]  Roger Lagunoff.  A Simple Noncooperative Core Story , 1994 .

[15]  John. Moore,et al.  Subgame Perfect Implementation , 1988 .

[16]  L. Hurwicz.  Studies in Resource Allocation Processes: Optimality and informational efficiency in resource allocation processes , 1977 .

[17]  Thomas R. Palfrey,et al.  Nash Implementation Using Undominated Strategies , 1991 .

[18]  Roberto Serrano,et al.  Non-cooperative implementation of the core , 1997 .

[19]  B. Moldovanu,et al.  Core implementation and increasing returns to scale for cooperation , 1994 .

[20]  Bezalel Peleg,et al.  Existence theorem for the bargaining set $M_1^{\left( i \right)}$ , 1963 .

[21]  Michael Maschler,et al.  An advantage of the bargaining set over the core , 1976 .

[22]  Arunava Sen,et al.  VIRTUAL IMPLEMENTATION IN NASH EQUILIBRIUM , 1991 .

[23]  A Consistent Bargainin , 1989 .

[24]  E. Maskin.  Nash Equilibrium and Welfare Optimality , 1999 .

[25]  Dilip Abreu,et al.  Subgame perfect implementation: A necessary and almost sufficient condition , 1990 .