Threshold uncertainty in the private-information subscription game

Abstract

We introduce threshold uncertainty,à la Nitzan and Romano (1990), into a private-values model of voluntary provision of a discrete public good. Players are allowed to make any level of contribution toward funding the good, which is provided only if the cost threshold is reached. Otherwise, contributions are refunded. Conditions ensuring existence and uniqueness of a Bayesian equilibrium are established. Further restricting the threshold uncertainty to a uniform distribution, we show the equilibrium strategies are very simple, even allowing for any number of players with asymmetric distributions of values. Comparative statics with respect to changes in players' distributions are derived, allowing changes in both the intensity and the dispersion of values. Finally, we show the equilibrium is interim incentive inefficient. The sharpness of our results greatly contrasts with the more qualified insights of earlier private-values models with known cost threshold, which relied on there being two symmetric players and generally exhibited multiple equilibria.JEL Codes: H41, D61, D82

Private Information in the BBV Model of Public Goods

“…Earlier works on this subject were limited in focusing primarily on equilibrium existence with two agents, since multiple equilibria typically exist and complicated strategies make deriving comparative statics results forbidding . The recent contribution of Barbieri and Malueg () adds threshold uncertainty to the discrete model with the result that equilibrium is unique, readily characterized, and easily amenable to comparative statics analysis and applications (see, e.g., Krasteva and Yildirim ; Barbieri and Malueg ), even for asymmetric environments with many agents. However, Barbieri and Malueg () operate in a binary public‐good, subscription‐game framework .…”

Changes in the Threshold Uncertainty in a Simultaneous Subscription Game

“…Barbieri and Malueg [11] include both threshold uncertainty and private information on public good valuations in the subscription game. They find that increased player valuation, in the sense of the first order stochastic dominance, or a more dispersed player value distribution, in the sense of a mean-preserving spread, increases the equilibrium contributions.…”

“…Barbieri and Malueg [11] assume the threshold uncertainty and private information in their model, but they only analyze the effects of changing the valuation distribution. Our paper complements these existing papers by investigating the comparative statics effect of changing the cost distribution on private contributions within a Barbieri and Malueg setting with both threshold uncertainty and private information.…”

On the voluntary provision of “weakest‐link” public goods: The case of private information

“…A general discussion of this issue, including a brief literature review, appears in Barbieri and Malueg ().…”

“…3 For an unambiguous improvement in costs, we shift cost distributions by first-order stochastic dominance (FOSD). 4 A general discussion of this issue, including a brief literature review, appears in Barbieri and Malueg (2010). 5 For theoretical analyses of technology transfer and learning in full-information environments, using different production functions than ours, also see Antonetti and Rufini (2008) and Jovanovic and Nyarko (1995), and references therein.…”