Nonlinear Duopoly Games with Advertisement∗

This study introduces advertisement into the dynamic nonlinear duopoly model. It demonstrates three major findings. The first is that the model can be destabilized via either flip bifurcation or Hopf bifurcation, the second is that a half-pitchfork bifurcation of output occurs when the advertisement dynamics is periodic and the nonlinearity of the output dynamics becomes stronger, and the third is that the existence of attractor and the coexistence of attracting sets are the main features of the model when it is locally unstable. ∗We highly appreciate finanical supports from the Japan Ministry of Education, Culture, Sports, Science and Technology (Grant-in-Aid for Scientific Research (A) 16203019) and the US Air Force Office of Scientific Research (MURI grant N14-03-1-150). We are also grateful to J. Minagawa for his supporting computational studies. †742-1, Higashi-Nakano, Hachioji, Tokyo, 192-0393, Japan. [email protected]; +81-426-74-3551 (tel); +81-426-74-3425 (fax). ‡Tucson, AZ, 85721-0020, USA. [email protected]; +01-520-621-6557 (tel); +01520-621-6555 (fax).