An Implementation-Theoretic Approach to Non-cooperative Foundations

Abstract The goal of non-cooperative foundations is to provide credible non-cooperative models of negotiation and coalition formation whose equilibrium outcomes agree with a given cooperative solution. Here we argue that this goal is best achieved by explicitly modeling the physical environment and individual preferences, and by constructing game forms independent of preferences to implement the cooperative solution. We propose a general model of the physical environment; we characterize the coalitional functions arising from environments via α - and β -effectivity; and we take up an issue of “payoff consistency” with special reference to the core. Journal of Economic Literature Classification Numbers: C71, C72, C78.

[1]  H. Moulin.  Implementing the Kalai-Smorodinsky bargaining solution , 1984 .

[2]  Walter Bossert,et al.  An arbitration game and the egalitarian bargaining solution , 1995 .

[3]  Robert W. Rosenthal,et al.  Cooperative games in effectiveness form , 1972 .

[4]  Tatsuyoshi Saijo,et al.  Toward Natural Implementation , 1996 .

[5]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[6]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[7]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

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

[9]  Debraj Ray,et al.  A noncooperative theory of coalitional bargaining , 1993 .

[10]  Roberto Serrano,et al.  A comment on the Nash program and the theory of implementation , 1997 .

[11]  B. Moldovanu,et al.  Order independent equilibria , 1995 .

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

[13]  R. E. Bixby,et al.  A characterization of polyhedral market games , 1973 .

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

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

[16]  Robert J. Aumann,et al.  Essays in game theory and mathematical economics in honor of Oskar Morgenstern , 1981 .

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

[18]  John. Moore,et al.  Nash Implementation: A Full Characterization , 1990 .

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

[20]  G. Owen,et al.  The Consistent Shapley Value for Games without Side Payments , 1992 .

[21]  R. Aumann,et al.  VON NEUMANN-MORGENSTERN SOLUTIONS TO COOPERATIVE GAMES WITHOUT SIDE PAYMENTS , 1960, Classics in Game Theory.

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

[23]  Tatsuro Ichiishi,et al.  The cooperative nature of the firm , 1994 .

[24]  J. Harsanyi.  An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition , 1974 .

[25]  R. Aumann.  The core of a cooperative game without side payments , 1961 .

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

[27]  Herbert E. Scarf,et al.  On the existence of a coopertive solution for a general class of N-person games☆ , 1971 .

[28]  Matthew O. Jackson,et al.  Undominated Nash Implementation in Bounded Mechanisms , 1994 .

[29]  R. Bixby,et al.  Market representations of $n$-person games , 1974 .

[30]  Yves Sprumont.  On the game-theoretic structure of public-good economies , 1997, Int. J. Game Theory.

[31]  J. Bergin.  A model of strategic behaviour in repeated games , 1992 .

[32]  A. Rubinstein.  Perfect Equilibrium in a Bargaining Model , 1982 .

[33]  J. V. Howard,et al.  A Social Choice Rule and its Implementation in Perfect Equilibrium (Now published in Journal of Economic Theory, 56 (1992), pp.142-159.) , 1992 .

[34]  J. Nash.  Two-Person Cooperative Games , 1953 .

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

[36]  T. Ichiishi.  A Social Coalitional Equilibrium Existence Lemma , 1981 .

[37]  Barton L. Lipman,et al.  Provision of Public Goods: Fully Implementing the Core through Private Contributions , 1989 .

[38]  Ehud Kalai,et al.  A group incentive compatible mechanism yielding core allocations , 1979 .

[39]  Arunava Sen,et al.  Nash implementation through elementary mechanisms in economic environments , 1994 .

[40]  A. Mas-Colell.  A further result on the representation of games by markets , 1975 .

[41]  Louis J. Billera,et al.  On games without side payments arising from a general class of markets , 1974 .

[42]  M. Shubik.  Game theory in the social sciences: Concepts and solutions , 1982 .

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

[44]  L. Shapley,et al.  ON MARKET GAMES , 1969, Classics in Game Theory.

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

[46]  John P. Conley,et al.  Implementing the nash extension bargaining solution for non-convex problems , 1994 .