Mathematical Programming

, Volume 104, Issue 2–3, pp 407–435 | Cite as

Collusive game solutions via optimization

  • J.E. Harrington
  • B.F. Hobbs
  • J.S. PangEmail author
  • A. Liu
  • G. Roch


A Nash-based collusive game among a finite set of players is one in which the players coordinate in order for each to gain higher payoffs than those prescribed by the Nash equilibrium solution. In this paper, we study the optimization problem of such a collusive game in which the players collectively maximize the Nash bargaining objective subject to a set of incentive compatibility constraints. We present a smooth reformulation of this optimization problem in terms of a nonlinear complementarity problem. We establish the convexity of the optimization problem in the case where each player's strategy set is unidimensional. In the multivariate case, we propose upper and lower bounding procedures for the collusive optimization problem and establish convergence properties of these procedures. Computational results with these procedures for solving some test problems are reported.

Mathematics Subject Classification (1991)

90C26 90C33 90C90 91A10 91A20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • J.E. Harrington
    • 1
  • B.F. Hobbs
    • 2
  • J.S. Pang
    • 3
    Email author
  • A. Liu
    • 4
  • G. Roch
    • 5
  1. 1.Department of EconomicsThe Johns Hopkins UniversityMarylandUSA
  2. 2.Department of Geography and Environmental EngineeringThe Johns Hopkins UniversityMarylandUSA
  3. 3.Department of Mathematical SciencesRensselaer Polytechnic InstituteNew YorkUSA
  4. 4.Department of Applied Mathematics and StatisticsThe Johns Hopkins UniversityMarylandUSA
  5. 5.Department of Applied Mathematics and StatisticsThe Johns Hopkins UniversityMarylandUSA

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