A fast algorithm to compute the Nash equilibrium for a two player positive game

Ivan G. Ivanov; Ivelin G. Ivanov

doi:10.1117/12.3011689

19 December 2023 A fast algorithm to compute the Nash equilibrium for a two player positive game

Ivan G. Ivanov, Ivelin G. Ivanov

Proceedings Volume 12936, International Conference on Mathematical and Statistical Physics, Computational Science, Education and Communication (ICMSCE 2023); 129360C (2023) https://doi.org/10.1117/12.3011689
Event: International Conference on Mathematical and Statistical Physics, Computational Science, Education and Communication (ICMSCE 2023), 2023, Istanbul, Turkey

Abstract

A linear quadratic differential game on an infinite time horizon with two types of an information structure is analysed and the equilibrium point is computed via stabilizing solution. The Newton solver for computing the stabilizing solution of the associated Nash-Riccati equations has been established. Here, a convergent linearized iterative method depending on a negative constant is introduced for each information structure: the open loop design and feedback design. The linearized iteration has a linear convergence rate, however there are cases where the iteration is faster than Newton's method. Numerical experiments are implemented to explain the computational advantages of the introduced solvers.

(2023) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Ivan G. Ivanov and Ivelin G. Ivanov "A fast algorithm to compute the Nash equilibrium for a two player positive game", Proc. SPIE 12936, International Conference on Mathematical and Statistical Physics, Computational Science, Education and Communication (ICMSCE 2023), 129360C (19 December 2023); https://doi.org/10.1117/12.3011689

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