<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

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

Foundations of Computing and Decision Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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...

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

Published Online: Jun 17, 2021

Page range: 173 - 197

Received: Jul 15, 2020

Accepted: Jan 22, 2021

DOI: https://doi.org/10.2478/fcds-2021-0012

Keywords
game theory, payoff functional, sinusoidal strategy, continuous game, finite approximation, attractive situation

© 2021 Vadim Romanuke, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Jun 17, 2021

Page range: 173 - 197

Received: Jul 15, 2020

Accepted: Jan 22, 2021

DOI: https://doi.org/10.2478/fcds-2021-0012

Keywordsgame theory, payoff functional, sinusoidal strategy, continuous game, finite approximation, attractive situation

© 2021 Vadim Romanuke, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
game theory, payoff functional, sinusoidal strategy, continuous game, finite approximation, attractive situation