Characterizing the Decidability of Finite State Automata Team Games with Communication

TL;DR

This paper investigates how limited communication affects the decidability of multiplayer team games with imperfect information, showing that below a certain communication rate, these games remain undecidable, but become decidable when the threshold is met.

Contribution

It introduces a new model of limited communication in team automata games and establishes the precise communication threshold for decidability.

Findings

Games are undecidable when communication rate is below move rate.

Games become decidable once communication reaches the move rate.

The model applies to bounded state automata team games.

Abstract

In this paper we define a new model of limited communication for multiplayer team games of imperfect information. We prove that the Team DFA Game and Team Formula Game, which have bounded state, remain undecidable when players have a rate of communication which is less than the rate at which they make moves in the game. We also show that meeting this communication threshold causes these games to be decidable.