Playing through a noisy channel (and knowing it)

TL;DR

This paper develops a theory of combinatorial games where moves are transmitted over noisy channels, affecting gameplay strategies and outcomes, with players aware of error probabilities and adapting their moves accordingly.

Contribution

It introduces a novel framework for combinatorial games that incorporates communication errors and analyzes strategic adaptations under noisy transmission conditions.

Findings

Basic definitions and results of noisy communication games

Examples illustrating game dynamics with errors

Strategies maximizing winning chances under noise

Abstract

In this note we discuss a theory of combinatorial games that involve transmitting the moves through a noisy channel that can introduce errors during the transmission. Players are aware of this interference and incorporate this variable into the game: the valid move is the received one, regardless of whether it is the other player's sent move (as long as it is a valid move in the original game; otherwise, a retransmission is requested). Players know the probability of introducing an error through communication and can play a non-optimal (but valid) move that maximizes their chances of winning. We present some examples and provide the basic definitions and results of this type of games.