The Game of Blocking Pebbles

TL;DR

The paper introduces Blocking Pebbles, a two-player variation of Graph Pebbling, analyzing its strategic complexity and identifying positions with diverse game values within Combinatorial Game Theory.

Contribution

It adapts Graph Pebbling into a two-player game and explores its game values, expanding understanding of its strategic and theoretical properties.

Findings

Positions with all integer values identified

Positions with all nimber values identified

Presence of infinitesimals and switches in game values

Abstract

Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory. Positions with game values matching all integers, all nimbers, and many infinitesimals and switches are found.