Completeness of Unbounded Best-First Game Algorithms

TL;DR

This paper proves the completeness of unbounded best-first game algorithms, including minimax and descent, and extends these results to multiplayer perfect information games, ensuring they find optimal strategies or equilibrium points given enough time.

Contribution

It establishes the completeness of unbounded best-first minimax and descent algorithms and generalizes these results to multiplayer perfect information games.

Findings

Proved completeness of unbounded best-first minimax with completion.

Proved completeness of descent with completion.

Generalized these algorithms to multiplayer perfect information games.

Abstract

In this article, we prove the completeness of the following game search algorithms: unbounded best-first minimax with completion and descent with completion, i.e. we show that, with enough time, they find the best game strategy. We then generalize these two algorithms in the context of perfect information multiplayer games. We show that these generalizations are also complete: they find one of the equilibrium points.