English

An Extension of the Normal Play Convention to $N$-player Combinatorial Games

Combinatorics 2019-03-05 v1

Abstract

We examine short combinatorial games for three or more players under a new play convention in which a player who cannot move on their turn is the unique loser. We show that many theorems of impartial and partizan two-player games under normal play have natural analogues in this setting. For impartial games with three players, we investigate the possible outcomes of a sum in detail, and determine the outcomes and structure of three-player Nim.

Keywords

Cite

@article{arxiv.1903.01375,
  title  = {An Extension of the Normal Play Convention to $N$-player Combinatorial Games},
  author = {Mark Spindler},
  journal= {arXiv preprint arXiv:1903.01375},
  year   = {2019}
}

Comments

45 pages; Presented at Integers Conference 2018, submitted to Proceedings