Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-Sided Altruism Dynamics-David Publishing Company
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Aoki Takaaki


Institute of Economics Research, Kyoto University


This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. The special case is analyzed where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. It is shown that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions of the class  with distinct steady states (indeterminacy of self-consistent, differentiable policy functions).


Bellman equation, Two-sided altruism, Dynamic inconsistency, Self-consistent policy functions, Indeterminacy, Overlapping generations model.

Cite this paper


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