The Myopic Stable Set for Social Environments (RM/17/002-revised)

We introduce a new solution concept for models of coalition formation, called the myopic stable set (MSS). The MSS is defined for a general class of social environments and allows for an infinite state space. An MSS exists and, under minor continuity assumptions, it is also unique. The MSS generalizes and unifies various results from more specific applications. It coincides with the coalition structure core in coalition function form games when this set is non-empty; with the set of stable matchings in the Gale-Shapley matching model; with the set of Pareto optimal allocations in the Shapley-Scarf housing matching model; with the set of pairwise stable networks and closed cycles in models of network formation; with the set of pure strategy Nash equilibria in pseudo-potential games and finite supermodular games; and with the set of mixed strategy Nash equilibria in several classes of two-player games.

[1]  P. Jean-Jacques Herings,et al.  Rationalizability for social environments , 2004, Games Econ. Behav..

[2]  William F. Lucas,et al.  Von Neumann-Morgenstern stable sets , 1992 .

[3]  Sylvain Béal,et al.  Accessibility and stability of the coalition structure core , 2013, Math. Methods Oper. Res..

[4]  M. Chwe.  Farsighted Coalitional Stability , 1994 .

[5]  Paul R. Milgrom,et al.  Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities , 1990 .

[6]  M. Jackson.  STABLE NETWORKS , 2000 .

[7]  Myrna Holtz Wooders,et al.  Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games , 2007, Games Econ. Behav..

[8]  Myrna Holtz Wooders,et al.  Networks and farsighted stability , 2005, J. Econ. Theory.

[9]  Guillermo Owen,et al.  Endogenous Formation of Coalitions , 2008, IGTR.

[10]  Akihisa Tamura,et al.  Transformation from Arbitrary Matchings to Stable Matchings , 1993, J. Comb. Theory, Ser. A.

[11]  Matthew O. Jackson,et al.  The Evolution of Social and Economic Networks , 2002, J. Econ. Theory.

[12]  Ad M. A. van Deemen,et al.  A note on generalized stable sets , 1991 .

[13]  D. M. Topkis.  Equilibrium Points in Nonzero-Sum n-Person Submodular Games , 1979 .

[14]  Ryoji Sawa,et al.  Coalitional stochastic stability in games, networks and markets , 2014, Games Econ. Behav..

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

[16]  W. F. Lucas,et al.  A Game with No Solution , 1968 .

[17]  M. K. Jensen.  Aggregative games and best-reply potentials , 2010 .

[18]  Pradeep Dubey,et al.  Strategic complements and substitutes, and potential games , 2006, Games Econ. Behav..

[19]  A. Roth,et al.  Random paths to stability in two-sided matching , 1990 .

[20]  Claudio Mezzetti,et al.  Better-reply dynamics and global convergence to Nash equilibrium in aggregative games , 2006, Games Econ. Behav..

[21]  P. Jean-Jacques Herings,et al.  Farsightedly Stable Networks , 2006, Games Econ. Behav..

[22]  Debraj Ray,et al.  Coalition formation as a dynamic process , 2003, J. Econ. Theory.

[23]  Anne van den Nouweland,et al.  Strongly Stable Networks , 2002, Games Econ. Behav..

[24]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

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

[26]  L. Shapley,et al.  Potential Games , 1994 .

[27]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[28]  Sayantan Ghosal,et al.  Farsighted network formation , 2005, J. Econ. Theory.

[29]  L. Xue,et al.  Coalitional stability under perfect foresight , 1998 .

[30]  H. Young,et al.  The Evolution of Conventions , 1993 .

[31]  Sanjeev Goyal,et al.  A Noncooperative Model of Network Formation , 2000 .

[32]  P. Jean-Jacques Herings,et al.  Stability of Networks Under Level-K Farsightedness , 2014 .

[33]  Luc Lauwers,et al.  The Coalition Structure Core is Accessible , 2001, Games Econ. Behav..

[34]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[35]  Hanna Bäck.  Coalition Formation and the Inclusion of Green Parties in Swedish Local Government , 2001 .

[36]  Claudio Mezzetti,et al.  Learning in Games by Random Sampling , 2001, J. Econ. Theory.

[37]  H. Scarf.  The Core of an N Person Game , 1967 .

[38]  Debraj Ray,et al.  The Farsighted Stable Set , 2013 .

[39]  L. Shapley,et al.  On cores and indivisibility , 1974 .

[40]  Mark Voorneveld,et al.  Best-response potential games , 2000 .

[41]  R. Rob,et al.  Learning, Mutation, and Long Run Equilibria in Games , 1993 .

[42]  A. Roth,et al.  The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design , 1999, The American economic review.

[43]  M. Jackson,et al.  A Strategic Model of Social and Economic Networks , 1996 .

[44]  P. Jean-Jacques Herings,et al.  Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance , 2016 .

[45]  Jacob D. Leshno,et al.  Unbalanced Random Matching Markets: The Stark Effect of Competition , 2017, Journal of Political Economy.