Partition Equilibrium

We introduce partition equilibrium and study its existence in resource selection games (RSG). In partition equilibrium the agents are partitioned into coalitions, and only deviations by the prescribed coalitions are considered. This is in difference to the classical concept of strong equilibrium according to which any subset of the agents may deviate. In resource selection games, each agent selects a resource from a set of resources, and its payoff is an increasing (or non-decreasing) function of the number of agents selecting its resource. While it has been shown that strong equilibrium exists in resource selection games, these games do not possess super-strong equilibrium, in which a fruitful deviation benefits at least one deviator without hurting any other deviator, even in the case of two identical resources with increasing cost functions. Similarly, strong equilibrium does not exist for that restricted two identical resources setting when the game is played repeatedly. We prove that for any given partition there exists a super-strong equilibrium for resource selection games of identical resources with increasing cost functions; we also show similar existence results for a variety of other classes of resource selection games. For the case of repeated games we identify partitions that guarantee the existence of strong equilibrium. Together, our work introduces a natural concept, which turns out to lead to positive and applicable results in one of the basic domains studied in the literature.

[1]  O. Rozenfeld.  Strong Equilibrium in Congestion Games , 2007 .

[2]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[3]  Paul G. Spirakis,et al.  Atomic congestion games among coalitions , 2008, TALG.

[4]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[5]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[6]  Mark Voorneveld,et al.  Congestion Games and Potentials Reconsidered , 1999, IGTR.

[7]  Itai Ashlagi,et al.  Social Context Games , 2008, WINE.

[8]  Yishay Mansour,et al.  Strong price of anarchy , 2007, SODA '07.

[9]  Robert J. Aumann,et al.  16. Acceptable Points in General Cooperative n-Person Games , 1959 .

[10]  Éva Tardos,et al.  The effect of collusion in congestion games , 2006, STOC '06.

[11]  Haim Kaplan,et al.  Strong Price of Anarchy for Machine Load Balancing , 2007, ICALP.

[12]  Yishay Mansour,et al.  Strong equilibrium in cost sharing connection games , 2007, EC '07.

[13]  Piotr Sankowski,et al.  Network formation games with local coalitions , 2007, PODC '07.

[14]  Fan Chung Graham,et al.  Internet and Network Economics, Third International Workshop, WINE 2007, San Diego, CA, USA, December 12-14, 2007, Proceedings , 2007, WINE.

[15]  L. Shapley,et al.  REGULAR ARTICLEPotential Games , 1996 .

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

[17]  Ron Holzman,et al.  Network structure and strong equilibrium in route selection games , 2003, Math. Soc. Sci..