Title: Game algebra: algebraic system of strategic-form games

Authors: Naoki Shiba

Addresses: College of Industrial Technology, Nihon University, 1-2-1 Izumicho, Narashino, Chiba, 275-8575, Japan

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.

Keywords: strategic form games; normal form games; abstract algebra; commutative groups; abelian groups; commutative monoids; complex decision problems; decomposition; game theory; mathematical modelling; strategic dominance; Nash equilibria.

DOI: 10.1504/AJMSA.2016.082968

Asian Journal of Management Science and Applications, 2016 Vol.2 No.4, pp.365 - 375

Received: 24 Feb 2016
Accepted: 21 Apr 2016
Published online: 17 Mar 2017 *

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