It is becoming more and more difficult for PhD graduates to find a job corresponding to their qualifications. Stephan and Levin have shown that this situation weakens the implicit contract between PhD students (or post-doc) and the research team in which they are doing their research. This weakness of the implicit contract may slow down scientific production because of the lack of incentives for good students to participate in academic science production. The aim of this paper is to examine incentives for students to invest in a PhD and for PhD supervisors to hire PhD students. After a theoretical analysis, hypotheses are made. These are tested by means of a survey on 400 engineering science PhD students from the University of Grenoble (a medium-sized town in France, with a large academic community). Do students with a Master's degree have relevant information about the scientific community and scientific rules to enable them to choose the “best” place to complete their PhD? What are the main factors determining their choice? Are trajectories flexible? To what extent is their research affected by these variables? In research, do private firms and academia have the same criteria when it comes to recruiting PhD graduates? The analysis shows that trajectories are not flexible and that PhD graduates have to choose a trajectory when their level of information is at its lowest. When they choose their first job after completing their PhD, the cost of switching from academia to the private sector or vice versa depends on whether or not they collaborated with the private sector during their PhD and on the intensity of publication. The existence of two sectors of recruitment with two sets of criteria to evaluate applicants' abilities can affect the implicit contract between PhD graduates and PhD supervisors and the dynamics of scientific production.