  Scientists pursue collective knowledge, but they also seek personal
recognition from their peers. When scientists decide whether or not to work on
a big new problem, they weigh the potential rewards of a major discovery
against the costs of setting aside other projects. These self-interested
choices can potentially spread researchers across problems in an efficient
manner, but efficiency is not guaranteed. We use simple economic models to
understand such decisions and their collective consequences. Academic science
differs from industrial R&D in that academics often share partial solutions to
gain reputation. This convention of Open Science is thought to accelerate
collective discovery, but we find that it need not do so. The ability to share
partial results influences which scientists work on a particular problem;
consequently, Open Science can slow down the solution of a problem if it deters
entry by important actors.
