On Pareto Optimality in Social Distance Games

We investigate Pareto stability in Social Distance Games, that are coalition forming games in which agents utilities are proportional to their harmonic centralities in the respective coalitions, i.e., to the average inverse distance from the other agents. Pareto optimal solutions have been already considered in the literature as outcomes arising from the strategic interaction of the agents. In particular, they are stable under the deviation of the grand coalition, as they do not permit a simultaneous deviation by all the agents making all of them weakly better off and some strictly better off. We first show that, while computing a Pareto stable solution maximizing the social welfare is NP-hard in bounded degree graphs, a 2min{Δ,√n}-approximating one can be determined in polynomial time, where n is the number of agents and Δ the maximum node degree. We then determine asymptotically tight bounds on the Price of Pareto Optimality for several classes of social graphs arising from the following combinations: unbounded and bounded node degree, undirected and directed edges, unweighted and weighted edges.

[1]  Tim Roughgarden,et al.  The price of stability for network design with fair cost allocation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[2]  Felix Brandt,et al.  Fractional Hedonic Games: Individual and Group Stability , 2015, AAMAS.

[3]  Michael Wooldridge,et al.  Hedonic coalition nets , 2009, AAMAS.

[4]  Simina Brânzei,et al.  Coalitional affinity games , 2009, AAMAS.

[5]  Joachim Gudmundsson,et al.  Welfare Maximization in Fractional Hedonic Games , 2015, IJCAI.

[6]  Kishan G. Mehrotra,et al.  A Game Theoretic Framework for Community Detection , 2012, 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining.

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

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

[9]  Angelo Fanelli,et al.  Price of Pareto Optimality in Hedonic Games , 2016, AAAI.

[10]  Martin Olsen,et al.  On defining and computing communities , 2012, CATS 2012.

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

[12]  Vittorio Bilò,et al.  On the Price of Stability of Fractional Hedonic Games , 2015, AAMAS.

[13]  Felix Brandt,et al.  Pareto Optimality in Coalition Formation , 2011, SAGT.

[14]  Sebastiano Vigna,et al.  Axioms for Centrality , 2013, Internet Math..

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

[16]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[17]  José R. Correa,et al.  Sloan School of Management Working Paper 4319-03 June 2003 Selfish Routing in Capacitated Networks , 2022 .

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

[19]  Simina Brânzei,et al.  Social Distance Games , 2011, IJCAI.

[20]  Vittorio Bilò,et al.  Nash Stability in Fractional Hedonic Games , 2014, WINE.