Bilinear Games: Polynomial Time Algorithms for Rank Based Subclasses

  • Jugal Garg
  • Albert Xin Jiang
  • Ruta Mehta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)


Motivated by the sequence form formulation of Koller et al. [16], this paper considers bilinear games, represented by two payoff matrices (A,B) and compact polytopal strategy sets. Bilinear games are very general and capture many interesting classes of games including bimatrix games, two player Bayesian games, polymatrix games, and two-player extensive form games with perfect recall as special cases, and hence are hard to solve in general. For a bilinear game, we define its best response polytopes (BRPs) and characterize its Nash equilibria as the fully-labeled pairs of the BRPs. Rank of a game (A,B) is defined as rank(A + B). In this paper, we give polynomial-time algorithms for computing Nash equilibria of (i) rank-1 games, (ii) FPTAS for constant-rank games, and (iii) when rank(A) or rank(B) is constant.


Nash Equilibrium Polynomial Time Algorithm Payoff Matrice Fully Polynomial Time Approximation Scheme Time Poly 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jugal Garg
    • 1
  • Albert Xin Jiang
    • 2
  • Ruta Mehta
    • 1
  1. 1.Indian Institute of TechnologyBombayIndia
  2. 2.University of British ColumbiaCanada

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