## Seminarios académicos y conferencias

### Lucas Maestri, (FGV/EPGE)

#### "A Continuous-Time Model of the Ratchet Effect"

Coautores: Mehmet Ekmekci y Leandro Gorno

27 Marzo 2018 - 17:00 hrs.

Sala 209, Facultad de Ciencias Económicas y Administrativas UC

Abstract: We study a continuous-time ratchet-effect model. An uninformed principal is uncertain about whether the agent is a commitment or a strategic type. The information about the agent’s type arrives continuously according to a diffusion process and the agent controls its mean. When a Poisson shock arrives, the principal decides whether to fire the agent (or take another irreversible action such as proposing worse terms of trade). The principal would like to fire the strategic type, but not the commitment type. The strategic agent’s myopic best response is an action different than the commitment’s (i.e., the strategic action), but he prefers imitating the commitment type (i.e., taking the commitment action) rather than being fired by the principal. The agent trade-offs the shortrun gains from taking the strategic action instead of the commitment action with the long-run reputation gains associated with delaying his eventual dismissal. We show that there is a unique smooth Markovian equilibrium. When the discount rate is high, the strategic agent always takes the strategic action, which rapidly decreases the agent’s expected reputation. When the discount rate is small, the agent takes the strategic action with probability one only when he enjoys a very small or very high reputation. Starting at a given initial belief, the agent starts mixing between the two actions as his reputation worsens. The probability that the commitment action is chosen by the agent increases as his reputation diminishes until the point in which the principal finds optimal to fire the agent whenever she has a chance. As the agent’s reputation further deteriorates, the probability that the strategic action is played increases. Any remaining incentives to play the commitment action fully disappear when the agent’s reputation is sufficiently bad.