This paper generalizes the classical discounted utility model introduced by Samuelson by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski's extension of the Banach Contraction Principle. The derived utilities...

In this paper we study a Markov decision process with a non-linear discount function. Our approach is in spirit of the von Neumann-Morgenstern concept and is based on the notion of expectation. First, we define a utility on the space of trajectories of the process in the finite and infinite time...

We consider zero-sum stochastic games with Borel state spaces satisfying a generalized geometric ergodicity condition. We prove under fairly general assumptions that the optimality equation has a solution which is unique up to an additive constant. Copyright Springer-Verlag Berlin Heidelberg 2001

Nonzero-sum ergodic semi-Markov games with Borel state spaces are studied. An equilibrium theorem is proved in the class of correlated stationary strategies using public randomization. Under some additivity assumption concerning the transition probabilities stationary Nash equilibria are also...

We consider semi-Markov control models (SMCMs) with a Borel state space satisfying certain stochastic stability assumptions on the transition structure which imply the so-called V-uniform geometric ergodicity of the state process. We deal with a class of ε-perturbations of transition...

We consider zero-sum stochastic games with Borel state spaces satisfying a generalized geometric ergodicity condition. We prove under fairly general assumptions that the optimality equation has a solution which is unique up to an additive constant. Copyright Springer-Verlag Berlin Heidelberg 2001

Nonzero-sum ergodic semi-Markov games with Borel state spaces are studied. An equilibrium theorem is proved in the class of correlated stationary strategies using public randomization. Under some additivity assumption concerning the transition probabilities stationary Nash equilibria are also...