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  • 1
    Electronic Resource
    Electronic Resource
    A note on strong 1-optimal policies in Markov decision chains with unbounded costs (1999)
    Springer
    Mathematical methods of operations research 49 (1999), S. 475-482 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Markov decision chains ; countable state space ; sensitive optimality ; unbounded costs.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We extend a result by Cavazos-Cadena and Lasserre on the existence of strong 1-optimal stationary policies in Markov decision chains with countable state spaces, uniformly ergodic transition probabilities and bounded costs to a larger class of models with unbounded costs and the so-called V-uniform ergodic transition structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050062
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  • 2
    Electronic Resource
    Electronic Resource
    Sensitive equilibria for ergodic stochastic games with countable state spaces (1999)
    Springer
    Mathematical methods of operations research 50 (1999), S. 65-76 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Stochastic games ; countable state space ; sensitive optimality ; unbounded payoffs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We consider stochastic games with countable state spaces and unbounded immediate payoff functions. Our assumptions on the transition structure of the game are based on a recent work by Meyn and Tweedie [19] on computable bounds for geometric convergence rates of Markov chains. The main results in this paper concern the existence of sensitive optimal strategies in some classes of zero-sum stochastic games. By sensitive optimality we mean overtaking or 1-optimality. We also provide a new Nash equilibrium theorem for a class of ergodic nonzero-sum stochastic games with denumerable state spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050035
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  • 3
    Electronic Resource
    Electronic Resource
    A counterexample on overtaking optimality (1999)
    Springer
    Mathematical methods of operations research 49 (1999), S. 435-439 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Markov decision chains ; overtaking optimality criteria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. Brown [3] constructed an aperiodic Markov decision chain in which no overtaking policy (stationary or nonstationary) exists. However, in his example a strong overtaking optimal policy exists in the class of all stationary policies. We provide another example of an aperiodic and geometric ergodic Markov decision chain which shows that the existence of a strong overtaking optimal stationary policy may fail inclusively in the class of stationary policies. We also give a brief survey of the existing literature on overtaking optimality in Markov decision chains.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050059
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    Paper (German National Licenses)
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