Persona: Prieto Rumeau, Tomás
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tprieto@ccia.uned.es
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0000-0003-4677-4725
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Prieto Rumeau
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Tomás
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Publicación Absorbing Markov decision processes(EDP Sciences, 2024-02-09) Dufour, François; Prieto Rumeau, TomásIn this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not occupation measures may exist. Several necessary and sufficient conditions are provided to guarantee that any solution to the characteristic equation is an occupation measure. Under the so-called continuity-compactness conditions, we first show that a measure is precisely an occupation measure if and only if it satisfies the characteristic equation and an additional absolute continuity condition. Secondly, it is shown that the set of occupation measures is compact in the weak-strong topology if and only if the model is uniformly absorbing. Several examples are provided to illustrate our results.Publicación Stationary Markov Nash equilibria for Nonzero-Sum constrained ARAT Markov Games(Society for Industrial and Applied Mathematics, 2022) Dufour, François; Prieto Rumeau, TomásWe consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a discounted payoff are satisfied. We are interested in the existence of a Nash or noncooperative equilibrium. Under suitable conditions, which include absolute continuity of the transitions with respect to some reference probability measure, additivity of the payoffs and the transition probabilities (ARAT condition), and continuity in action of the payoff functions and the density function of the transitions of the system, we establish the existence of a constrained stationary Markov Nash equilibrium, that is, the existence of stationary Markov strategies for each of the players yielding an optimal profile within the class of all history-dependent profiles.Publicación Maximizing the probability of visiting a set infinitely often for a countable state space Markov decision process(Elsevier, 2022-01-15) Dufour, François; Prieto Rumeau, TomásWe consider a Markov decision process with countable state space and Borel action space. We are interested in maximizing the probability that the controlled Markov chain visits some subset of the state space infinitely often. We provide sufficient conditions, based on continuity and compactness requirements, together with a stability condition on a parametrized family of auxiliary control models, which imply the existence of an optimal policy that is deterministic and stationary. We compare our hypotheses with those existing in the literature.Publicación Nash equilibria for total expected reward absorbing Markov games: The constrained and unconstrained cases(Springer Nature, 2024-01-17) Dufour, François; Prieto Rumeau, TomásWe consider a nonzero-sum N -player Markov game on an abstract measurable state space with compact metric action spaces. The payoff functions are bounded Carathéodory functions and the transitions of the system are assumed to have a density function satisfying some continuity conditions. The optimality criterion of the players is given by a total expected payoff on an infinite discrete-time horizon. Under the condition that the game model is absorbing, we establish the existence of Markov strategies that are a noncooperative equilibrium in the family of all history-dependent strategies of the players for both the constrained and the unconstrained problems. We obtain, as a particular case of results, the existence of Nash equilibria for discounted constrained and unconstrained game models.