Merger dynamics in three-agent games

Regular Article Interdisciplinary Physics


We present the effect of mergers, a term which we use to mean a temporary alliance, in the dynamics of the three-agent model studied by Ben-Naim, Kahng and Kim and by Rador and Mungan. Mergers are possible in three-agent games because two agents can combine forces against the third player and thus increase their probability to win a competition. We implement mergers in this three-agent model via resolving merger and no-merger units of competition in terms of a two-agent unit. This way one needs only a single parameter which we have called the competitiveness parameter. We have presented an analytical solution in the fully competitive limit. In this limit the score distribution of agents is stratified and self-similar.


Selection Rule Riemann Problem Shift Symmetry Large Point Equal Likelihood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    E. Ben-Naim, F. Vazquez, S. Redner, Eur. Phys. J. B 26, 531 (2006) ADSCrossRefGoogle Scholar
  2. 2.
    E. Ben-Naim, F. Vazquez, S. Redner, J. Quant. Anal. Sports 2 (2006) Google Scholar
  3. 3.
    E. Ben-Naim, F. Vazquez, S. Redner, J. Korean Phys. Soc. 50, 124 (2006) Google Scholar
  4. 4.
    E. Ben-Naim, B. Kahng, J.S. Kim, J. Stat. Mech. P07001 (2006) Google Scholar
  5. 5.
    T. Rador, M. Mungan, J. Phys. A: Math. Theor. 41, 055002 (2008) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    P.D. Lax, Hyperbolic Partial Differential Equations, Courant Lecture Notes (2006), Vol. 14, ISBN-13: 978-0-8218-3576-0 Google Scholar
  7. 7.
    T. Liu, K. Nishihara, J. Differ. Equ. 133, 296 (1997) MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    T. Liu, A. Matsumura, K. Nishihara, SIAM J. Math. Anal. 29, 293 (1998) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    T. Nakamura, SIAM J. Math. Anal. 34, 1308 (2003) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    D.M. Kilgour, S.J. Brams, Mathematics Magazine 70, 315 (1997) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Physics BebekBog̃aziçi UniversityİstanbulTurkey
  2. 2.Department of Physics Urlaİzmir Institute of TechnologyİzmirTurkey
  3. 3.İş Bankası, İş Kuleler, Kule 1 LeventİstanbulTurkey

Personalised recommendations