Abstract
In this paper, we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish sufficient conditions under which the value function satisfies the Dynamic Programming Principle.
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- 1.
From an economic point of view, the constraint can be interpreted as an incentive to respect some contract. In this sense we are in a normative perspective. A social planner seeks an optimal policy among those not including the termination of the process. The goal is the definition of a social contract, whose breach is prevented by the incentive compatibility constraint.
- 2.
We recall that in Barucci et al. (2000) the set \(\mathbb {X}\) is one of the unknown to be found.
- 3.
The functional \(J_{g_{2}}(x;\cdot )\) is comonotone with respect to J r (x; ⋅) when for all controls \(c_{1},c_{2}\in \mathcal {C}_{g}(x)\) the condition
$$\displaystyle \begin{aligned} J_{r}(x;c_{1})\leq J_{r}(x;c_{2}) \end{aligned}$$implies
$$\displaystyle \begin{aligned} J_{g_{2}}(x;c_{1})\leq J_{g_{2}}(x;c_{2}). \end{aligned}$$Clearly, the same holds for \(J_{g_{2}}^{h}(x;\cdot )\)
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Gozzi, F., Monte, R., Tessitore, M.E. (2018). On the Dynamic Programming Approach to Incentive Constraint Problems. In: Feichtinger, G., Kovacevic, R., Tragler, G. (eds) Control Systems and Mathematical Methods in Economics. Lecture Notes in Economics and Mathematical Systems, vol 687. Springer, Cham. https://doi.org/10.1007/978-3-319-75169-6_5
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DOI: https://doi.org/10.1007/978-3-319-75169-6_5
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