Multiplicity and uniqueness in dynamic decision problems

Dynamic decision-making without commitment is usually modelled as a game between the current and future selves of the decision-maker. It has been observed that if the time-horizon is infinite, then such games may have multiple subgame-perfect equilibrium solutions. We show that such multiplicity arises in an open set of stochastic dynamic programming problems with minimal non-trivial stateand action spaces, under arbitrary quasi-exponential discounting. We also provide a sufficient condition for uniqueness for infinitely repeated decision problems that is, when there is only one state for a wide class of discount functions and arbitrary action spaces.