On the bi-extremal bi-stabilization of a cooperative game in product space N1 × N2

Abstract

In this research paper, we aim to expand the scope of cooperative game theory from its traditional domain in N to the more versatile cartesian product N1 ×N2. This extension allows us to explore the intriguing possibility of players collaborating in multiple games simultaneously. Within this context, we introduce several fundamental concepts in game theory that apply to the cartesian product N1 × N2, such as coalition, cooperative games, core solution, and other essential notions. Additionally, we present the innovative bi-extremal bi-stabilization algorithm, a powerful computational tool designed to address maximization problems within the cartesian product N1 × N2.