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Partially-Observed Bilinear Nonzero-Sum Stochastic Differential Game with Affine-Quadratic Discounted Payoff and Application to Competitive Advertising

Author

Listed:
  • Wang Tao

    (Guangdong University of Technology)

  • Cheng-Ke Zhang

    (Guangdong University of Technology)

  • Lu Yang

    (Guangdong Polytechnic Normal University)

Abstract

In this paper, an affine-quadratic stochastic differential game in bilinear system is introduced to formulate a sales advertising problem with discounted payoff and noisy observer. Firstly, the two-person nonzero-sum game is consolidated into a standard bilinear framework, then Nash equilibrium is approximated by iterative algorithm and the convergence is proved. Some extensions of the separation theorem for nonlinear system are provided to solve the partially-observed stochastic differential game. The bilinear dynamics on competitive advertising is widely adopted in the lecture and represents a challenging problems in mathematical derivation. An iterative stimulation scheme with filter is designed for automatic solutions. The modeling of noisy observer and the discounted payoffs as a more realistic application is illustrated with simulation results.

Suggested Citation

  • Wang Tao & Cheng-Ke Zhang & Lu Yang, 2024. "Partially-Observed Bilinear Nonzero-Sum Stochastic Differential Game with Affine-Quadratic Discounted Payoff and Application to Competitive Advertising," Dynamic Games and Applications, Springer, vol. 14(2), pages 453-479, May.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:2:d:10.1007_s13235-023-00535-6
    DOI: 10.1007/s13235-023-00535-6
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