A firm is seeking to fill a single position that demands a highly specialized skill set such that only two

candidates satisfy the minimal requirements. Each candidate i $=1,2$ invests time ti in $[0,$ T $]$ at a cost c$($ti$)$ to

produce an application of quality q$($ti$),$ where T $>0$ is the application deadline and c and q are continuous,

increasing functions with c$(0)=$ q$(0)=0.$ The firm hires the applicant with the better application, with ties

broken equally among them. Applicants are risk$-$neutral and value the