Theory of Computing Systems

, Volume 59, Issue 3, pp 440–475 | Cite as

Assignment Games with Conflicts: Robust Price of Anarchy and Convergence Results via Semi-Smoothness

  • Elliot AnshelevichEmail author
  • John Postl
  • Tom Wexler


We study assignment games in which jobs select machines, and in which certain pairs of jobs may conflict, which is to say they may incur an additional cost when they are both assigned to the same machine, beyond that associated with the increase in load. Questions regarding such interactions apply beyond allocating jobs to machines: when people in a social network choose to align themselves with a group or party, they typically do so based upon not only the inherent quality of that group, but also who amongst their friends (or enemies) chooses that group as well. We show how semi-smoothness, a recently introduced generalization of smoothness, is necessary to find tight bounds on the robust price of anarchy, and thus on the quality of correlated and Nash equilibria, for several natural job-assignment games with interacting jobs. For most cases, our bounds on the robust price of anarchy are either exactly 2 or approach 2. We also prove new convergence results implied by semi-smoothness for our games. Finally we consider coalitional deviations, and prove results about the existence and quality of strong equilibrium.


Price of anarchy Group formation Smooth games Congestion games Cut games Games in networks 



This work was supported in part by NSF grants CCF-0914782, CCF-1101495, and CNS-1017932. We thank Carlos Varela for illuminating discussions on the subject of job assignment.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Rensselaer Polytechnic InstituteTroyUSA
  2. 2.Oberlin CollegeOberlinUSA

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