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Artykuł


Tytuł

Acceptable-and-attractive Approximate Solution of a Continuous Non-Cooperative Game on a Product of Sinusoidal Strategy Functional Spaces

Autorzy

Rok publikacji

2021

Opublikowano w

Foundations of Computing and Decision Sciences

Rocznik: 2021 | Tom: vol. 46 | Numer: no. 2

Typ artykułu

artykuł naukowy

Język publikacji

angielski

Słowa kluczowe
EN
  • game theory
  • payoff functional
  • sinusoidal strategy
  • continuous game
  • finite approximation
  • attractive situation
Streszczenie

EN A problem of solving a continuous noncooperative game is considered, where the player’s pure strategies are sinusoidal functions of time. In order to reduce issues of practical computability, certainty, and realizability, a method of solving the game approximately is presented. The method is based on mapping the product of the functional spaces into a hyperparallelepiped of the players’ phase lags. The hyperparallelepiped is then substituted with a hypercubic grid due to a uniform sampling. Thus, the initial game is mapped into a finite one, in which the players’ payoff matrices are hypercubic. The approximation is an iterative procedure. The number of intervals along the player’s phase lag is gradually increased, and the respective finite games are solved until an acceptable solution of the finite game becomes sufficiently close to the same-type solutions at the preceding iterations. The sufficient closeness implies that the player’s strategies at the succeeding iterations should be not farther from each other than at the preceding iterations. In a more feasible form, it implies that the respective distance polylines are required to be decreasing on average once they are smoothed with respective polynomials of degree 2, where the parabolas must be having positive coefficients at the squared variable.

Strony (od-do)

173 - 197

DOI

10.2478/fcds-2021-0012

URL

https://sciendo.com/article/10.2478/fcds-2021-0012

Typ licencji

CC BY-NC-ND (uznanie autorstwa - użycie niekomercyjne - bez utworów zależnych)

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