On Algorithms for Simple Stochastic Games (1993)
| Venue: | Advances in Computational Complexity Theory, volume 13 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science |
| Citations: | 49 - 1 self |
BibTeX
@INPROCEEDINGS{Condon93onalgorithms,
author = {Anne Condon},
title = {On Algorithms for Simple Stochastic Games},
booktitle = {Advances in Computational Complexity Theory, volume 13 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science},
year = {1993},
pages = {51--73},
publisher = {American Mathematical Society}
}
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Abstract
We survey a number of algorithms for the simple stochastic game problem, which is to determine the winning probability of a type of stochastic process, where the transitions are partially controlled by two players. We show that four natural approaches to solving the problem are incorrect, and present two new algorithms for the problem. The first reduces the problem to that of finding a locally optimal solution to a (non-convex) quadratic program with linear constraints. The second extends a technique of Shapley called the successive approximation technique, by using linear programming to maximize the improvement at each approximation step. Finally, we analyze a randomized variant of the Hoffman-Karp strategy improvement algorithm. 1 Introduction In this paper, we study algorithms for the simple stochastic game problem. The problem is to find the winning probability of a type of stochastic process where transitions are partially controlled by two players. A simple stochastic game is a ...
