Highly lopsided information and the Borel hierarchy

TL;DR

This paper explores the limits of perfect information in games, focusing on when a player with super-perfect information can guarantee a win in a hierarchy of lopsided-information guessing games.

Contribution

It provides an exact characterization of winning strategies for the player with super-perfect information in a specific class of lopsided guessing games.

Findings

Identifies conditions for guaranteed winning strategies

Establishes a hierarchy of information levels in games

Connects game theory with the Borel hierarchy

Abstract

In a game where both contestants have perfect information, there is a strict limit on how perfect that information can be. By contrast, when one player is deprived of all information, the limit on the other player's information disappears, admitting a hierarchy of levels of lopsided perfection of information. We turn toward the question of when the player with super-perfect information has a winning strategy, and we exactly answer this question for a specific family of lopsided-information games which we call guessing games.