Top guns may not fire: Best-shot group contests with group-specific public good prizes

We analyze a group contest in which n groups compete to win a group-specific public good prize. Group sizes can be different and any player may value the prize differently within and across groups. Players exert costly efforts simultaneously and independently. Only the highest effort (the best-shot) within each group represents the group effort that determines the winning group. We fully characterize the set of equilibria and show that in any equilibrium at most one player in each group exerts strictly positive effort. There always exists an equilibrium in which only the highest value player in each active group exerts strictly positive effort. However, perverse equilibria may exist in which the highest value players completely free-ride on others by exerting no effort. We provide conditions under which the set of equilibria can be restricted and discuss contest design implications.