Game algebra: algebraic system of strategic-form games
by Naoki Shiba
Asian J. of Management Science and Applications (AJMSA), Vol. 2, No. 4, 2016

Abstract: In game theory, a 'game' is a system in which two or more decision makers interact with each other. This article proposes and investigates the properties of a new approach, which we call 'game algebra', which represents the strategic form (or normal form) of a game as an algebraic entity. In game theory, the representation of games as mathematical models allows them to be treated as algebraic entities in a way similar to the algebra of relational database theory. In game algebra, we regard the coupling of two games in strategic form as an algebraic operation. We prove that these operations preserve various game solution properties, such as strategic dominance and Nash equilibria. We show that a class of n-person games in strategic form are a commutative (abelian) group and a commutative monoid.

Online publication date: Mon, 13-Mar-2017

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the Asian J. of Management Science and Applications (AJMSA):
Login with your Inderscience username and password:

    Username:        Password:         

Forgotten your password?


Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com