Step-by-step group contests with group-specific public-good prizes

The achievements reached by group members' effort, which accompanies the possibility of members' free-riding, affect the outcomes of competition among groups. In some cases, each achievement has the binary characteristic of one or nothing. For example, research groups face the challenge of making a scientific finding or not. The groups compete for a scientific breakthrough by making the related findings in a step-by-step manner. One finding could fail because of a mistake caused by a slight lack of effort by one member. Such a characteristic of one or nothing motivates group members without any incentive scheme. This study analyzes group contests with group-specific public-good prizes, in which we introduce a step function with the characteristics of one or nothing and step-by-step as a group impact function. We show the existence of the Nash equilibrium at which no group member free-rides on the others and at which more achievements than those reachable by a single member are reached.