Non-cooperative games with minmax objectives

  • Francisco Facchinei
  • Jong-Shi Pang
  • Gesualdo Scutari


We consider noncooperative games where each player minimizes the sum of a smooth function, which depends on the player, and of a possibly nonsmooth function that is the same for all players. For this class of games we consider two approaches: one based on an augmented game that is applicable only to a minmax game and another one derived by a smoothing procedure that is applicable more broadly. In both cases, centralized and, most importantly, distributed algorithms for the computation of Nash equilibria can be derived.


Nash equilibrium problem Nondifferentiable objective function Distributed algorithm Smoothing 



The authors thank two referees who have offered constructive comments that have improved the presentation of the paper. In particular, one referee has provided additional references, including [38], that are related to our work. The work of the second author was based on research supported by the U.S.A. National Science Foundation Grant CMMI–0969600 while the work of the third author was based on research supported by the U.S.A. National Science Foundation CNS–1218717 and CAREER Grant #1254739


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Francisco Facchinei
    • 1
  • Jong-Shi Pang
    • 2
  • Gesualdo Scutari
    • 3
  1. 1.Department of Computer, Control, and Management Engineering Antonio RubertiUniversity of Rome La SapienzaRomeItaly
  2. 2.Deptartment of Industrial and Systems EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of Electrical EngineeringState University of New York (SUNY) at BuffaloBuffaloUSA

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