Strategic equivalence among hat puzzles of various protocols with many colors

TL;DR

This paper explores complex hat puzzles involving infinitely many prisoners and multiple colors, establishing strategic equivalences among various protocols when hat colors form a commutative group.

Contribution

It introduces a framework for analyzing infinite prisoner hat puzzles with multiple colors using group theory, proving strategic equivalence among different protocols.

Findings

Established strategic equivalence among protocols with countably many prisoners

Extended analysis to puzzles with infinitely many colors and prisoners

Utilized commutative group structure to unify different puzzle strategies

Abstract

We discuss ``puzzles of prisoners and hats`` with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of several protocols with countably many prisoners.