Bray Theory Workshop
Abstract
We study a collaboration model in continuous time, with a positive arrival rate of a success in both the good and the bad state. If the project is bad, players may privately learn about it. At any time, players can choose whether to exit and secure the positive payoff of an outside option, or to stay with the project and exert costly effort. A player's effort not only increases the probability of success, but also serves as an investment in private learning.
We identify an equilibrium with three phases. In all phases, uninformed players exert positive effort. Players who become informed and learn that the project is bad never exert effort. Because players benefit from the effort of the others, informed players may not exit immediately. In the first, "no-exit" phase, informed players do not exit. In the subsequent, "gradual-exit" phase, they exit with a finite rate. In the final, "immediate-exit" phase, informed players exit immediately. We find that effort levels may increase in the no-exit phase, if the markup of effort in the bad state is positive. Surprisingly, increasing the payoff of the outside option encourages collaboration.