The determinacy of infinite games with eventual perfect monitoring

TL;DR

This paper proves that infinite two-player zero-sum games with Borel winning sets are determined even when monitoring is delayed, by representing them as stochastic games with perfect information and applying Martin's Theorem.

Contribution

It introduces a novel approach to establish determinacy for games with eventual monitoring by modeling them as stochastic games with perfect information.

Findings

Games with eventual perfect monitoring are determined.

Representation as stochastic games facilitates the proof.

Utilizes Martin's Theorem for determinacy.

Abstract

n infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, is determined. The proof relies on a representation of the game as a stochastic game with perfect information, in which Chance operates as a delegate for the players and performs the randomizations for them, and on Martin's Theorem about the determinacy of such games.