This paper studies the endogenous timing of moves in a game with competition in basic research between a university and a commercial firm. It examines the conditions under which the two entities end up investing in innovation at equilibrium, both under simultaneous and sequential moves. It argues that when the innovation process is not too costly, under any timing, the firm conducts research despite the opportunities for complete free riding. The two sequential move games with either player as leader emerge as equilibrium endogenous timings, with both entities realizing higher profits in either outcome than in a simultaneous move game. Each entity also profits more by following than by leading. Finally, as a proxy for a welfare analysis, we compare the propensities for innovation across the three scenarios and find that university leadership yields a superior performance. This may be used as a selection criterion to choose the latter scenario as the unique outcome of endogenous timing.