Abstract
In this paper we analyze a three-period dynamic investment model where a principal interacts with an agent who is time-inconsistent. We use βδ-preferences to capture time-inconsistency. In every period, the agent invests an amount and then the principal, observing the investment amount, makes an offer or not; finally the agent accepts the offer or not. For both the sophisticated agent (who is aware of his inconsistency) and the naive agent (who is not aware of his inconsistency), we find the optimal investment streams. The difference in their information set is causing them to finalize the game at different periods or to attain different levels of investments. We found that the naive agent ends up investing a higher (or equal) overall amount than the sophisticated agent, and thus the principal is (weakly) better off with a naive agent.
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