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A Theory of Self-Prospection
A present-biased decision maker (DM) faces a two-armed bandit problem whose risky arm generates random payoffs at exponentially distributed times. The DM learns about payoff arrivals through informative feedback. At the unique stationary Markov perfect equilibrium of the multi-self game, positive feedback supports greater equilibrium welfare than both negative and transparent feedback. Regardless of the form of feedback, the DM's behavior exhibits indecision, deriving from their desire to procrastinate. We relate our findings to the theory of self-prospection -- the process of imagining future goals and outcomes when seeking motivation in the present.