Implementation of Bargaining Sets via Simple Mechanisms

Abstract We propose two simple mechanisms that implement two bargaining sets in super-additive environments. The first bargaining set is a close variation of the one proposed by L. Zhou (1994, Games Econom. Behav. 6 , 512–526), and the second is the Pareto optimum payoffs of the A. Mas-Colell (1989, J. Math. Econom. 18 , 129–139) bargaining set. We adopt a simple framework in which the cooperative outcomes are realized as non-cooperative subgame perfect equilibria in pure strategies of a two-stage game played by an auxiliary set of individuals competing over the cooperative agents. Journal of Economic Literature Classification Numbers: C71, C72.

[1]  Rajiv Vohra,et al.  An existence theorem for a bargaining set , 1991 .

[2]  A. Rubinstein,et al.  The Structure of Nash Equilibrium in Repeated Games with Finite Automata (Now published in Econometrica, 56 (1988), pp.1259-1282.) , 1986 .

[3]  A. W. Tucker,et al.  Advances in game theory , 1964 .

[4]  D. Monderer,et al.  A 2£ 2 Game without the Fictitious Play Property ⁄ , 1996 .

[5]  Lin Zhou,et al.  A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation , 1994 .

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

[7]  David Wettstein,et al.  A non-cooperative interpretation of bargaining sets , 1999 .

[8]  Two Characterizations of Bargaining Sets , 1992 .

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

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

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

[12]  R. Stearns.  Convergent transfer schemes for $N$-person games , 1968 .

[13]  Ron Holzman,et al.  On the Least Core and the Mas-Colell Bargaining Set , 1999 .

[14]  J. Pérez-Castrillo,et al.  Cooperative Outcomes through Noncooperative Games , 1994 .

[15]  M. Maschler,et al.  Stable Sets and Stable Points of Set-Valued Dynamic Systems with Applications to Game Theory , 1976 .

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

[17]  M. Maschler.  The bargaining set, kernel, and nucleolus , 1992 .

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

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

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