Matching with myopic and farsighted players

Abstract We introduce the new notion of the pairwise myopic-farsighted stable set to study stable matchings under the assumption that players can be both myopic and farsighted. For the special case where all players are myopic, our concept predicts the set of matchings in the core. When all players are farsighted, we provide the characterization of pairwise myopic-farsighted stable sets: a set of matchings is a pairwise myopic-farsighted stable set if and only if it is a singleton consisting of a core element. This result confirms the result obtained by Mauleon, Vannetelbosch and Vergote (2011) with a completely different effectivity function and provides a new special case where the farsighted stable set is absolutely maximal ( Ray and Vohra, 2019 ) and coincides with the Strong Rational Expectations Farsighted Stable Set ( Dutta and Vohra, 2017 ). When myopic and farsighted players interact, matchings outside the core can be stable and the most farsighted side can achieve its optimal stable matching.

[1]  Licun Xue,et al.  Farsighted Stability in Hedonic Games , 2000 .

[2]  Debraj Ray,et al.  The Farsighted Stable Set , 2015 .

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

[4]  Wouter Vergote,et al.  Von Neumann-Morgenstern Farsightedly Stable Sets in Two-Sided Matching , 2008 .

[5]  Elena Molis,et al.  Dominance invariant one-to-one matching problems , 2014, Int. J. Game Theory.

[6]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

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

[8]  Ana Mauleon,et al.  Stability of networks under horizon-K farsightedness , 2019 .

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

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

[11]  Rajiv Vohra,et al.  Maximality in the Farsighted Stable Set , 2019 .

[12]  Christian Seel,et al.  The Myopic Stable Set for Social Environments , 2019 .

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

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

[15]  James S. Jordan,et al.  Pillage and property , 2006, J. Econ. Theory.

[16]  Bhaskar Dutta,et al.  Coalition formation and history dependence , 2020 .

[17]  M. Utku Ünver,et al.  Credible group stability in many-to-many matching problems , 2006, J. Econ. Theory.

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

[19]  F. Echenique,et al.  A Theory of Stability in Many-to-Many Matching Markets , 2004 .

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

[21]  Bhaskar Dutta,et al.  Rational Expectations and Farsighted Stability , 2017 .

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

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

[24]  Lars Ehlers,et al.  Von Neumann-Morgenstern stable sets in matching problems , 2007, J. Econ. Theory.

[25]  A. Mauleon,et al.  Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers , 2003 .

[26]  L. Shapley,et al.  College Admissions and the Stability of Marriage , 1962 .

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

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

[29]  Jun Wako,et al.  A Polynomial-Time Algorithm to Find von Neumann-Morgenstern Stable Matchings in Marriage Games , 2010, Algorithmica.

[30]  Anne van den Nouweland,et al.  Farsighted stability with heterogeneous expectations , 2020, Games Econ. Behav..