Player preferences in $N$-player games

TL;DR

This paper explores player preferences in multi-player games, especially three-player scenarios, and demonstrates how these preferences can simplify game trees using Clobber as an example, though generalization remains challenging.

Contribution

It introduces a framework for understanding player preferences in N-player games and applies it to simplify game trees, highlighting specific cases and challenges for future work.

Findings

Short games can be simplified to a value in a concise set using fixed starting players.

Player preferences help reduce complexity in game tree analysis.

Generalizing to more than three players remains an open challenge.

Abstract

In this paper we describe several player preferences in games with $N \geq 2$ players, in particular the case $N = 3$, and use them to simplify game trees, using the game of Clobber as our example. We show that, using a fixed starting player and a certain ruleset, any short game can be simplified to a value in a very concise set. Omitting the fixed starting player and generalising the theory to more than 3 players remains a challenge.