Competitive problem solving and the optimal prize schemes

Agents compete to solve a problem. Each agent simultaneously chooses either a safe method or a risky method to solve the problem. This paper analyzes a prize scheme as an incentive to induce the optimal risk-taking level which maximizes the designerʼs interest. It is shown that whenever the winner-take-all scheme induces excessive risk-taking, there exists a prize scheme which induces the optimal risk-taking. Moreover, the existence of such a prize scheme is guaranteed if the number of competitors is sufficiently large.