Zero-Sum Average Cost Semi-Markov Games with Weakly Continuous Transition Probabilities and a Minimax Semi-Markov Inventory Problem

Óscar Vega-Amaya*, Fernando Luque-Vásquez, Mauricio Castro-Enríquez

*Autor correspondiente de este trabajo

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

1 Cita (Scopus)

Resumen

Under the framework given by a growth condition, a Lyapunov property and some continuity assumptions, the present work shows the existence of lower semicontinuous solutions to the Shapley equation for zero-sum semi-Markov games with Borel spaces, weakly continuous transition probabilities and possible unbounded payoff. It is also shown the existence of stationary optimal strategies for the minimizing player and stationary ε-optimal strategies for the maximizing player. These results are proved using a fixed-point approach. Moreover, it is shown the existence of a deterministic stationary minimax strategy for a minimax semi-Markov inventory problem under mild assumptions on the demand distribution.

Idioma originalInglés
Número de artículo9
PublicaciónActa Applicandae Mathematicae
Volumen177
N.º1
DOI
EstadoPublicada - feb. 2022

Nota bibliográfica

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.

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