Weakest-link contests with group-specific public good prizes

We examine the equilibrium effort levels of individual players and groups in contests in which n group compete to win a group-specific public good prize, individual players choose their effort levels simultaneously and independently, and each group's probability of winning the prize follows a weakest-link rule or weakest-link contest success function. In our basic model, we show that the lowest-valuation players in each group play decisive roles in determining the Nash equilibria of the game. There are multiple pure-strategy Nash equilibria in the game but there is a unique coalition-proof Nash equilibrium at which neither any player nor any group does not have an incentive to coordinate and deviate from the equilibrium. No free riding problem exists in equilibrium. As an example of our basic model, we consider a simple contest where two groups with two players compete against, and find that the high-valuation players in each group have incentives to subsidize the low-valuation players in their group. Finally, we examine the equilibrium subsidy rates of the groups in a contest where first the high-valuation players in each group decide how much to subsidize low-valuation players in their group and then the individual players in the contest choose their effort levels simultaneously and independently.