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The Markov decision processes under quasi-hyperbolic discounting are studied. This type of discounting nicely models human behaviour, which is time-inconsistent in the long run. The decision maker has preferences changing in time. Therefore, the standard approach based on the Bellman optimality principle fails. Within a dynamic game-theoretic framework, the existence of randomised stationary Markov perfect equilibria for a large class of Markov decision processes with transitions having a density function is proved. Moreover, under some additional conditions, this equilibrium can be replaced by a deterministic one. During the talk many examples will be discussed to illustrate our results, including a portfolio selection model with quasi-hyperbolic discounting.