Markov perfect equilibria for risk-sensitive Markov decision processes with quasi-hyperbolic discounting

We investigate a discrete-time Markov decision model in which the decision maker aggregates utilities determined along every infinite history of the process using quasi-hyperbolic discounting. To evaluate this aggregated utility, he applies a certainty equivalent with respect to the probability measure on the space of all paths induced by the transition probabilities and a strategy profile. Since such a dynamic decision model exhibits time inconsistency, we apply a well-established game theoretic approach. The solution concept is called a Markov perfect equilibrium and is time-consistent.