4 research outputs found
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A pseudo-polynomial algorithm for mean payoff stochastic games with perfect information and few random positions
We consider two-person zero-sum stochastic mean payoff games with perfect information,
or BWR-games, given by a digraph G = (V;E), with local rewards r : E Z, and three
types of positions: black VB, white VW, and random VR forming a partition of V . It is a long-
standing open question whether a polynomial time algorithm for BWR-games exists, or not,
even when |VR| = 0. In fact, a pseudo-polynomial algorithm for BWR-games would already
imply their polynomial solvability. In this paper, we show that BWR-games with a constant
number of random positions can be solved in pseudo-polynomial time. More precisely, in any
BWR-game with |VR| = O(1), a saddle point in uniformly optimal pure stationary strategies
can be found in time polynomial in |VW| + |VB|, the maximum absolute local reward, and the
common denominator of the transition probabilities
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A potential reduction algorithm for two-person zero-sum mean payoff stochastic games
We suggest a new algorithm for two-person zero-sum undiscounted
stochastic games focusing on stationary strategies. Given a positive real
, let us call a stochastic game -ergodic, if its values from any two initial
positions dier by at most . The proposed new algorithm outputs for
every > 0 in nite time either a pair of stationary strategies for the two
players guaranteeing that the values from any initial positions are within
an -range, or identies two initial positions u and v and corresponding
stationary strategies for the players proving that the game values starting
from u and v are at least =24 apart. In particular, the above result
shows that if a stochastic game is -ergodic, then there are stationary
strategies for the players proving 24-ergodicity. This result strengthens
and provides a constructive version of an existential result by Vrieze (1980)
claiming that if a stochastic game is 0-ergodic, then there are -optimal
stationary strategies for every > 0. The suggested algorithm is based
on a potential transformation technique that changes the range of local
values at all positions without changing the normal form of the game
Recommended from our members
A potential reduction algorithm for two-person zero-sum mean payoff stochastic games
We suggest a new algorithm for two-person zero-sum undiscounted
stochastic games focusing on stationary strategies. Given a positive real
, let us call a stochastic game -ergodic, if its values from any two initial
positions dier by at most . The proposed new algorithm outputs for
every > 0 in nite time either a pair of stationary strategies for the two
players guaranteeing that the values from any initial positions are within
an -range, or identies two initial positions u and v and corresponding
stationary strategies for the players proving that the game values starting
from u and v are at least =24 apart. In particular, the above result
shows that if a stochastic game is -ergodic, then there are stationary
strategies for the players proving 24-ergodicity. This result strengthens
and provides a constructive version of an existential result by Vrieze (1980)
claiming that if a stochastic game is 0-ergodic, then there are -optimal
stationary strategies for every > 0. The suggested algorithm is based
on a potential transformation technique that changes the range of local
values at all positions without changing the normal form of the game
Recommended from our members
A potential reduction algorithm for two-person zero-sum mean payoff stochastic games
We suggest a new algorithm for two-person zero-sum undiscounted
stochastic games focusing on stationary strategies. Given a positive real
, let us call a stochastic game -ergodic, if its values from any two initial
positions dier by at most . The proposed new algorithm outputs for
every > 0 in nite time either a pair of stationary strategies for the two
players guaranteeing that the values from any initial positions are within
an -range, or identies two initial positions u and v and corresponding
stationary strategies for the players proving that the game values starting
from u and v are at least =24 apart. In particular, the above result
shows that if a stochastic game is -ergodic, then there are stationary
strategies for the players proving 24-ergodicity. This result strengthens
and provides a constructive version of an existential result by Vrieze (1980)
claiming that if a stochastic game is 0-ergodic, then there are -optimal
stationary strategies for every > 0. The suggested algorithm is based
on a potential transformation technique that changes the range of local
values at all positions without changing the normal form of the game