Some Classes of Imperfect Information
Finite State-Space Stochastic
Games with Finite-Dimensional Solutions |
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Authors: | Email author" target="_blank">William M?McEneaneyEmail author |
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Institution: | (1) Departments of Mathematics and Mechanical/Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093-0112, USA |
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Abstract: | Stochastic games under imperfect information are typically
computationally intractable even in the discrete-time/discrete-state
case considered here. We consider a problem where one
player has perfect information.
A function of a conditional probability
distribution is proposed as an information state.
In the problem form here, the payoff is
only a function of the terminal state of the system,
and the initial information state is either linear or
a sum of max-plus delta functions.
When the initial information state belongs to these
classes, its propagation is finite-dimensional.
The state feedback value function is also finite-dimensional,
and obtained via dynamic programming,
but has a nonstandard form
due to
the necessity of an expanded state variable.
Under a saddle point assumption,
Certainty Equivalence is obtained and the proposed function
is indeed an information state. |
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Keywords: | Dynamic games Stochastic games Imperfect information Certainty equivalence Markov chains |
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