A Recursive Algorithm for Solving Simple Stochastic Games

10/03/2021

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by   Xavier Badin de Montjoye, et al.

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We present two recursive strategy improvement algorithms for solving simple stochastic games. First we present an algorithm for solving SSGs of degree d that uses at most O(⌊(d+1)^2/2⌋^n/2) iterations, with n the number of MAX vertices. Then, we focus on binary SSG and propose an algorithm that has complexity O(φ^nPoly(N)) where φ = (1 + √(5))/2 is the golden ratio. To the best of our knowledge, this is the first deterministic strategy improvement algorithm that visits 2^cn strategies with c < 1.