Cookie Monster Plays Games

TL;DR

This paper introduces the Cookie Monster game, a combinatorial game generalizing Nim and Wythoff, analyzes P-positions, and explores related intermediate games from both narrative and formal perspectives.

Contribution

It presents the Cookie Monster game, extends the family of combinatorial games, and studies their P-positions with novel insights and characterizations.

Findings

Characterization of P-positions in Cookie Monster game

Introduction of intermediate games between Nim and Cookie Monster

Insights into the structure and properties of these combinatorial games

Abstract

We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and Nim. We discuss properties of P-positions of all of these games. Each section consists of two parts. The first part is a story presented from the Cookie Monster's point of view, the second part is a more abstract discussion of the same ideas by the authors.