Profit-Maximizing Sale of a Discrete Public Good: linear equilibria in the private information subscription game. Working paper, available at: http://www.economics.ucr.edu/seminars/winter08/ets/Barbieri-Malueg.pdf

We analyze a symmetric Bayesian game in which two players individually contribute to fund a dis-crete public good; contributions are refunded if they do not meet a threshold set by the seller of the good. We provide a general characterization of symmetric equilibrium strategies that are continuous and nonconstant over the set of values for which the good has a positive chance of provision. Piecewise-linear strategies are our special focus. We characterize the distributions of players ’ private values that can support a continuous piecewise-linear symmetric equilibrium, and we calculate such equilibria for these distributions. Allowing the seller to charge a nonrefundable entry fee before players make their private contributions, we show these piecewise-linear equilibria can maximize the seller’s expected profit over all incentive compatible selling mechanisms