Completeness of Unbounded Best-First Game Algorithms

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.

Learning to Play Stochastic Two-player Perfect-Information Games without Knowledge

“…We now formalize the concept of determinization of a stochastic game. For this we recall the definition of deterministic two-player zero-sum games of (Cohen-Solal, 2021).…”