218 research outputs found
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 differ by at most . The proposed new algorithm
outputs for every in finite time either a pair of stationary
strategies for the two players guaranteeing that the values from any initial
positions are within an -range, or identifies two initial positions
and and corresponding stationary strategies for the players proving
that the game values starting from and are at least
apart. In particular, the above result shows that if a stochastic game is
-ergodic, then there are stationary strategies for the players
proving -ergodicity. This result strengthens and provides a
constructive version of an existential result by Vrieze (1980) claiming that if
a stochastic game is -ergodic, then there are -optimal stationary
strategies for every . 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
Player aggregation in the traveling inspector model
We consider a model of dynamic inspection/surveillance of
a number of facilities in different geographical locations. The inspector in
this process travels from one facility to another and performs an
inspection at each facility he visits. His aim is to devise an inspection/
travel schedule which minimizes the losses to society (or to his employer)
resulting both from undetected violations of the regulations and from the
costs of the policing operation. This model is formulated as a non-cooperative,
single-controller, stochastic game. The existence of stationary Nash
equilibria is established as a consequence of aggregating all the inspectees
into a single “aggregated inspectee”. It is shown that such player
aggregation causes no loss of generality under very mild assumptions. A
notion of an “optimal Nash equilibrium” for the inspector is introduced
and proven to be well-defined in this context. The issue of the inspector’s
power to “enforce” such an equilibrium is also discussed
Successive approximations for the average Markov reward game : the communicating case
This paper considers the two-person zero-sum Markov game with finite state and action spaces at the criterion of average reward per unit time. For two types of Markov games, the communicating game and the simply connected game, it is shown that the method of successive approximations provides good bounds on the value of the game and nearly-optimal stationary strategies for the two players
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
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
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
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