Private Learning and Exit Decisions in Collaboration

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
pay-off 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. Surprisingly, increasing the payoff of the outside option encourages collaboration.

Anne-Katrin Roesler is a microeconomic theorist interested in game theory, mechanism design and information economics. She received her Ph.D. in economics (2015), and a diploma in mathematics (2010) from the University of Bonn, Germany. She was a postdoctoral researcher at Kellogg School of Management, Northwestern University, 2015-2016, and spent a year visiting Yale University during her Ph.D. Her current research focuses on private learning in teams, and on information design questions. The latter aims to understand how to design the information environment of self-interested agents to best achieve a desired objective.