Auctioning Public Goods to Groups of Agents

A prot-maximizing auctioneer can provide a public good to at most one of a
number of groups of agents. The groups may have non-empty intersections. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group with the highest sum of the agents' bids, only if this sum exceeds a minimum price declared previously by the auctioneer. For the one-group two-bidder case with private values drawn from a uniform distribution we characterize the continuously dierentiable symmetric equilibrium bidding functions for the agents, and nd the optimal minimum price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the dierentiable bidding functions.