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    Wyświetlanie 1-7 z 7
    Tytuł:
    Nonzero-sum semi-Markov games with countable state spaces
    Autorzy:
    Połowczuk, Wojciech
    Powiązania:
    https://bibliotekanauki.pl/articles/1208131.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    discounted criterion
    Nash equilibrium
    countable state space
    nonzero-sum semi-Markov game
    long run average reward criterion
    Opis:
    We consider nonzero-sum semi-Markov games with a countable state space and compact metric action spaces. We assume that the payoff, mean holding time and transition probability functions are continuous on the action spaces. The main results concern the existence of Nash equilibria for nonzero-sum discounted semi-Markov games and a class of ergodic semi-Markov games with the expected average payoff criterion.
    Źródło:
    Applicationes Mathematicae; 2000, 27, 4; 395-402
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonparametric adaptive control for discrete-time Markov processes with unbounded costs under average criterion
    Autorzy:
    Minjárez-Sosa, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/1338768.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Markov control process
    discounted and average cost criterion
    adaptive policy
    Opis:
    We introduce average cost optimal adaptive policies in a class of discrete-time Markov control processes with Borel state and action spaces, allowing unbounded costs. The processes evolve according to the system equations $x_{t+1}=F(x_t,a_t,ξ _t)$, t=1,2,..., with i.i.d. $ℝ^k$-valued random vectors $ξ_t$, which are observable but whose density ϱ is unknown.
    Źródło:
    Applicationes Mathematicae; 1999, 26, 3; 267-280
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximations of dynamic Nash games with general state and action spaces and ergodic costs for the players
    Autorzy:
    Bielecki, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/1339277.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    two-person game
    ε-Nash equilibrium
    sequential game
    long-run average criterion
    Opis:
    The purpose of this paper is to prove existence of an ε -equilib- rium point in a dynamic Nash game with Borel state space and long-run time average cost criteria for the players. The idea of the proof is first to convert the initial game with ergodic costs to an ``equivalent" game endowed with discounted costs for some appropriately chosen value of the discount factor, and then to approximate the discounted Nash game obtained in the first step with a countable state space game for which existence of a Nash equilibrium can be established. From the results of Whitt we know that if for any ε > 0 the approximation scheme is selected in an appropriate way, then Nash equilibrium strategies for the approximating game are also ε -equilibrium strategies for the discounted game constructed in the first step. It is then shown that these strategies constitute an ε -equilibrium point for the initial game with ergodic costs as well. The idea of canonical triples, introduced by Dynkin and Yushkevich in the control setting, is adapted here to the game situation.
    Źródło:
    Applicationes Mathematicae; 1996-1997, 24, 2; 195-202
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sample path average optimality of Markov control processes with strictly unbounded cost
    Autorzy:
    Vega-Amaya, Oscar
    Powiązania:
    https://bibliotekanauki.pl/articles/1338680.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    strictly unbounded costs
    sample path average cost criterion
    inventory systems
    Markov control processes
    Opis:
    We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover, we show that if such a policy induces a positive Harris recurrent Markov chain, then it is also sample path average (SPAC-) optimal. We apply our results to inventory systems and, in a particular case, we compute explicitly a deterministic stationary SPAC-optimal policy.
    Źródło:
    Applicationes Mathematicae; 1999, 26, 4; 363-381
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On approximations of nonzero-sum uniformly continuous ergodic stochastic games
    Autorzy:
    Nowak, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/1338847.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Nash equilibrium
    general state space
    nonzero-sum Markov game
    long run average reward criterion
    Opis:
    We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].
    Źródło:
    Applicationes Mathematicae; 1999, 26, 2; 221-228
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal stationary policies inrisk-sensitive dynamic programs with finite state spaceand nonnegative rewards
    Autorzy:
    Cavazos-Cadena, Rolando
    Montes-de-Oca, Raúl
    Powiązania:
    https://bibliotekanauki.pl/articles/1208177.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    unichain property
    Markov decision processes
    risk-sensitive optimality equation
    risk-sensitive expected total- reward criterion
    Opis:
    This work concerns controlled Markov chains with finite state space and nonnegative rewards; it is assumed that the controller has a constant risk-sensitivity, and that the performance ofa control policy is measured by a risk-sensitive expected total-reward criterion. The existence of optimal stationary policies isstudied within this context, and the main resultestablishes the optimalityof a stationary policy achieving the supremum in the correspondingoptimality equation, whenever the associated Markov chain hasa unique positive recurrent class. Two explicit examples are providedto show that, if such an additional condition fails, an optimal stationarypolicy cannot be generally guaranteed. The results of this note, which consider both the risk-seeking and the risk-averse cases, answer an extended version of a question recently posed in Puterman (1994).
    Źródło:
    Applicationes Mathematicae; 2000, 27, 2; 167-185
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some remarks on equilibria in semi-Markov games
    Autorzy:
    Nowak, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/1208130.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    correlated equilibrium
    Nash equilibrium
    general state space
    nonzero-sum semi-Markov game
    long run expected average payoff criterion
    Opis:
    This paper is a first study of correlated equilibria in nonzero-sum semi-Markov stochastic games. We consider the expected average payoff criterion under a strong ergodicity assumption on the transition structure of the games. The main result is an extension of the correlated equilibrium theorem proven for discounted (discrete-time) Markov games in our joint paper with Raghavan. We also provide an existence result for stationary Nash equilibria in the limiting average payoff semi-Markov games with state independent and nonatomic transition probabilities. A similar result was proven for discounted Markov games by Parthasarathy and Sinha.
    Źródło:
    Applicationes Mathematicae; 2000, 27, 4; 385-394
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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