Dynamics in matching and coalition formation games with structural constraints

Abstract Matching and coalition formation are fundamental aspects in the organization of many multi-agent systems. In large populations, the emergence of coalitions is often restricted by structural constraints under which agents can reorganize, e.g., local visibility or externality constraints among the agents. We study this aspect using a novel framework for dynamics with constraints within the popular domain of hedonic coalition formation games. We analyze the effects of structural constraints on the convergence of matching and coalition formation processes to stable states. Our main result are tight characterizations for the constraint structures based on which dynamic coalition formation can stabilize quickly. We show a variety of convergence results for matching and coalition formation games with different forms of locality and externality constraints. In particular, we propose and analyze a new model of graph-based visibility for coalition formation games and tightly characterize the graph structures that allow polynomial-time convergence – it can be achieved if and only if coalition formation is based on complete or star graphs.

[1]  Sergei Vassilvitskii,et al.  Social Networks and Stable Matchings in the Job Market , 2009, WINE.

[2]  Rahul Savani,et al.  Computing Stable Outcomes in Hedonic Games , 2010, SAGT.

[3]  Robert W. Irving.  An Efficient Algorithm for the "Stable Roommates" Problem , 1985, J. Algorithms.

[4]  Ramamohan Paturi,et al.  Jealousy Graphs: Structure and Complexity of Decentralized Stable Matching , 2013, WINE.

[5]  Felix Brandt,et al.  Optimal Partitions in Additively Separable Hedonic Games , 2011, IJCAI.

[6]  D. Levine.  Modeling Altruism and Spitefulness in Experiments , 1998 .

[7]  David Manlove,et al.  The Stable Roommates Problem with Globally Ranked Pairs , 2007, WINE.

[8]  Tamás Fleiner,et al.  The dynamics of stable matchings and half-matchings for the stable marriage and roommates problems , 2008, Int. J. Game Theory.

[9]  Robert W. Irving,et al.  The Stable marriage problem - structure and algorithms , 1989, Foundations of computing series.

[10]  Paul Harrenstein,et al.  Fractional Hedonic Games , 2014, AAMAS.

[11]  Petr A. Golovach,et al.  Solutions for the stable roommates problem with payments , 2012, Theor. Comput. Sci..

[12]  Edith Elkind,et al.  Hedonic Games with Graph-restricted Communication , 2016, AAMAS.

[13]  Dominik Peters.  Towards Structural Tractability in Hedonic Games , 2016, AAAI.

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

[15]  Marina Thottan,et al.  Market sharing games applied to content distribution in ad hoc networks , 2004, IEEE Journal on Selected Areas in Communications.

[16]  Edith Elkind,et al.  Simple Causes of Complexity in Hedonic Games , 2015, IJCAI.

[17]  F. Mathieu.  Acyclic Preference-Based Systems , 2010 .

[18]  J. Ledyard.  Public Goods: A Survey of Experimental Research , 1994 .

[19]  Martin Hoefer,et al.  Hedonic Coalition Formation in Networks , 2015, AAAI.

[20]  Stefano Leucci,et al.  Locality-based network creation games , 2014, SPAA.

[21]  Alvin E. Roth,et al.  Pairwise Kidney Exchange , 2004, J. Econ. Theory.

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

[23]  Martin Hoefer,et al.  Altruism in Atomic Congestion Games , 2013, TEAC.

[24]  G. Owen.  Values of graph-restricted games , 1986 .

[25]  Martin Hoefer.  Local matching dynamics in social networks , 2013, Inf. Comput..

[26]  Roger Wattenhofer,et al.  On Finding Better Friends in Social Networks , 2012, SSS.

[27]  Gerhard J. Woeginger,et al.  Core Stability in Hedonic Coalition Formation , 2012, SOFSEM.

[28]  Christine T. Cheng.  On the Stable Matchings That Can Be Reached When the Agents Go Marching in One By One , 2016, SIAM J. Discret. Math..

[29]  Matthew O. Jackson,et al.  The Stability of Hedonic Coalition Structures , 2002, Games Econ. Behav..

[30]  Martin Hoefer,et al.  Stable Matching with Network Externalities , 2017, Algorithmica.

[31]  David Manlove,et al.  Algorithmics of Matching Under Preferences , 2013, Bull. EATCS.

[32]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

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

[34]  Eric McDermid,et al.  Maximum Locally Stable Matchings , 2013, Algorithms.

[35]  Tayfun Sönmez,et al.  Core in a simple coalition formation game , 2001, Soc. Choice Welf..

[36]  Po-An Chen,et al.  Altruism and Its Impact on the Price of Anarchy , 2014, TEAC.

[37]  Martin Hoefer,et al.  Matching Dynamics with Constraints , 2014, WINE.

[38]  Uriel G. Rothblum,et al.  "Timing Is Everything" and Marital Bliss , 2002, J. Econ. Theory.

[39]  Martin Hoefer,et al.  Considerate Equilibrium , 2011, IJCAI.

[40]  J. Drèze,et al.  HEDONIC COALITIONS: OPTIMALITY AND STABILITY , 1980 .

[41]  Fabien Mathieu,et al.  Self-stabilization in preference-based systems , 2008, Peer-to-Peer Netw. Appl..

[42]  Eiichi Miyagawa,et al.  Random paths to stability in the roommate problem , 2004, Games Econ. Behav..

[43]  U. Rothblum,et al.  Vacancy Chains and Equilibration in Senior-Level Labor Markets , 1997 .

[44]  Dominik Peters,et al.  Complexity of Hedonic Games with Dichotomous Preferences , 2016, AAAI.

[45]  David Manlove,et al.  Socially Stable Matchings in the Hospitals/Residents Problem , 2013, WADS.

[46]  Jana Hajduková,et al.  Coalition Formation Games: a Survey , 2006, IGTR.

[47]  Vahab S. Mirrokni,et al.  Uncoordinated two-sided matching markets , 2009, SECO.

[48]  Haris Aziz,et al.  Existence of stability in hedonic coalition formation games , 2012, AAMAS.

[49]  Dominik Peters,et al.  Graphical Hedonic Games of Bounded Treewidth , 2016, AAAI.

[50]  Rahul Savani,et al.  Hedonic Games , 2016, Handbook of Computational Social Choice.

[51]  Jörg Rothe,et al.  Altruistic Hedonic Games , 2016, AAMAS.

[52]  Katarína Cechlárová.  Stable Partition Problem , 2016, Encyclopedia of Algorithms.

[53]  Martin Hoefer,et al.  Social Context in Potential Games , 2012, WINE.

[54]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[55]  Péter Biró,et al.  Analysis of stochastic matching markets , 2013, Int. J. Game Theory.

[56]  Kemal Akkaya,et al.  Autonomous actor positioning in wireless sensor and actor networks using stable-matching , 2010, Int. J. Parallel Emergent Distributed Syst..

[57]  Martin Hoefer,et al.  Locally Stable Marriage with Strict Preferences , 2012, SIAM J. Discret. Math..