Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
We introduce a patent (prize) which induces entry at a level which satisfies the basic condition of optimality with respect to the 'size' of the race (a second best patent). We observe that for the Lee-Wilde model of a patent race the second best prize induces approximately the socially optimal (first best) outcome. The approach of the second best patent provides one explanation for why discoverers should only receive a fraction of the ex post social value of their discovery.