Optimal Feedback in Contests.

This article focuses on designing optimal dynamic contests where a principal incentivizes multiple agents to exert costly effort monitored only through coarse, binary signals called Poisson successes, aiming to maximize total effort given a fixed prize. It establishes that any contest maximizing effort must feature a history-dependent termination rule, a feedback policy that immediately informs agents of their own successes (denoted as the \(\mathcal{M}^{\rm pronto}\) feedback), and a prize-allocation rule granting each successful agent a constant expected share equal to the cost-to-success ratio \(c/\lambda\). Among such contests, a special family termed "2nd chance" contests uniquely minimizes expected contest duration by continuing until a pre-specified number \(K^* = \lfloor \lambda/c \rfloor\) of successes occur, then entering a countdown phase giving remaining agents a final opportunity to succeed. The article further demonstrates robustness of these results to extensions including multiple successes per agent, heterogeneous success rates, increasing hazard rates, and limited principal commitment, and contrasts these contests with no-feedback fixed-deadline designs where an egalitarian prize split is optimal. Applications discussed include innovation races, promotion tournaments, and athletic qualifying stages, where effort is imperfectly monitored and successes are discrete.