The Ordered Join of Impartial Games

TL;DR

This paper introduces a new way to combine impartial games inspired by poset game theory, providing a comprehensive analysis using Sprague-Grundy theory and exploring its computational properties.

Contribution

It presents a novel compound of impartial games, complete analysis framework, and substitution and reduction principles, advancing the theoretical understanding of game combinations.

Findings

Complete analysis of the new game compound

Substitution and reduction principles established

Insights into computational complexity of the compound

Abstract

Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction principles for this compound and consider its computational aspects.