The Complexity of Mean Payoff Games on Graphs

  title={The Complexity of Mean Payoff Games on Graphs},
  author={Uri Zwick and Mike Paterson},
  journal={Electron. Colloquium Comput. Complex.},
  • U. Zwick, M. Paterson
  • Published 20 May 1996
  • Computer Science, Mathematics
  • Electron. Colloquium Comput. Complex.
The Complexity of Solving Stochastic Games on Graphs
A linear time algorithm is exhibited that given a simple stochastic game and the values of all positions of that game, computes a pair of optimal strategies.
The complexity of mean payoff games using universal graphs
It is shown that separating automata do not yield a quasipolynomial algorithm for solving mean payoff games, and tight bounds on the complexity of algorithms in this class are proved.
Faster algorithms for mean-payoff games
A new pseudopolynomial algorithm is presented for solving two-player games played on a weighted graph with mean-payoff objective and with energy constraints, improving the best known worst-case complexity for pseudopoly Nominal mean- payoff algorithms.
Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games
It is shown that the linear dependence in the exponent in the number k of weights implies that universal graphs do not yield a quasipolynomial time algorithm for solving mean payoff games, implying that tight bounds on the complexity of algorithms formean payoff games using universal graphs are proved.
The Complexity of Ergodic Mean-payoff Games
An optimal exponential bound on the patience of stationary strategies is established and the exact value can be expressed in the existential theory of the reals, and square-root sum hardness is established for a related class of games.
On the computational complexity of solving stochastic mean-payoff games
We consider some well-known families of two-player, zero-sum, perfect information games that can be viewed as special cases of Shapley's stochastic games. We show that the following tasks are
The complexity of ergodic games
We study finite-state two-player (zero-sum) concurrent mean-payoff games played on a graph. We focus on the important sub-class of ergodic games where all states are visited infinitely often with
On strategy improvement algorithms for simple stochastic games
The computational complexity of a strategy improvement algorithm by Hoffman and Karp for simple stochastic games is studied, and a bound of O(2^n/n) on the convergence time of the Hoffman-Karp algorithm, and the first non-trivial upper bounds on the converge time of these strategy improvement algorithms are proved.
On Strategy Improvement Algorithms for Simple Stochastic Games
The Hoffman-Karp algorithm converges to optimal strategies of a given SSG, but no nontrivial bounds were previously known on its running time, and a bound of O(2n/n) on the convergence time of this algorithm is shown, and these are the first non-trivial upper bounds on the converge time of these strategy improvement algorithms.
Combinatorial structure and randomized subexponential algorithms for infinite games


Complexity of Path-Forming Games
  • H. Bodlaender
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 1993
Cyclical games with prohibitions
This work proves the existence of optimal uniform stationary strategies for both cases of the price function and gives algorithms to find such strategies.
The Complexity of Stochastic Games
  • A. Condon
  • Mathematics, Computer Science
    Inf. Comput.
  • 1992
Undirected Edge Geography
A Subexponential Randomized Algorithm for the Simple Stochastic Game Problem
  • W. Ludwig
  • Computer Science, Mathematics
    Inf. Comput.
  • 1995
We describe a randomized algorithm for the simple stochastic game problem that requires 2O(?n) expected operations for games with n vertices. This is the first subexponential time algorithm for this
Positional strategies for mean payoff games
We study some games of perfect information in which two players move alternately along the edges of a finite directed graph with weights attached to its edges. One of them wants to maximize and the
A characterization of the minimum cycle mean in a digraph
  • R. Karp
  • Computer Science, Mathematics
    Discret. Math.
  • 1978
Stochastic Games*
  • L. Shapley
  • Medicine, Mathematics
    Proceedings of the National Academy of Sciences
  • 1953
In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players, and the expected total gain or loss is bounded by M, which depends on N 2 + N matrices.