Game Derandomization

TL;DR

This paper advances the theoretical understanding of game derandomization by providing improved bounds on Kolmogorov complexity for deterministic and probabilistic games, extending to various environment types and game classes.

Contribution

It introduces new upper bounds for Kolmogorov complexity in game derandomization and generalizes results to probabilistic, time-bounded, and all zero-sum repeated games.

Findings

Improved upper bounds for Kolmogorov complexity of winning players.

Generalization of derandomization results to probabilistic and uncomputable environments.

Characterization of partial game derandomization and classic even-odds game.

Abstract

Using Kolmogorov Game Derandomization, upper bounds of the Kolmogorov complexity of deterministic winning players against deterministic environments can be proved. This paper gives improved upper bounds of the Kolmogorov complexity of such players. This paper also generalizes this result to probabilistic games. This applies to computable, lower computable, and uncomputable environments. We characterize the classic even-odds game and then generalize these results to time bounded players and also to all zero-sum repeated games. We characterize partial game derandomization. But first, we start with an illustrative example of game derandomization, taking place on the island of Crete.