The complexity of solving reachability games using value and strategy iteration
Computer Science and Game Theory
2012-03-02 v3
Abstract
Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations needed by both of these algorithms for providing non-trivial approximations to the value of a game with N non-terminal positions and m actions for each player in each position. In particular, both algorithms have doubly-exponential complexity. Even when the game given as input has only one non-terminal position, we prove an exponential lower bound on the worst case number of iterations needed to provide non-trivial approximations.
Cite
@article{arxiv.1007.1812,
title = {The complexity of solving reachability games using value and strategy iteration},
author = {Kristoffer Arnsfelt Hansen and Rasmus Ibsen-Jensen and Peter Bro Miltersen},
journal= {arXiv preprint arXiv:1007.1812},
year = {2012}
}