PaperLink (coming soon)
We study a dynamic collective action problem where a group of n players secures a public good if at least mn of its members voluntarily commit to a costly action, whose cost is privately observed. Players contribute over time and the group succeeds in the first period when the number of volunteers exceeds m. For the special case of m=1, this game can be seen as a discrete-time version of the standard war of attrition; but it diverges in the general dynamic collective action problem when m>1. When m=1, types unravel over time and the collective good is eventually secured with probability one if its value is higher than the private cost of at least one individual, in which case the ex-ante allocation is inefficient only because of delay. Furthermore, the inefficiency due to delay vanishes as n→∞. In sharp contrast, all Perfect Bayesian Equilibria in the dynamic collective action problem (m>1) “get stuck”. That is, with positive probability, contributions will stop short of the threshold at some finite date τ, even if all individual costs are strictly lower than the value of the public good. The equilibrium outcomes however have a simple characterization in large populations: welfare converges to either full efficiency or zero depending on a condition on the growth rate of mn that we characterize. Delay is therefore irrelevant: in the limit either the good is achieved in period 1 with probability close to 1, or it is as if it is never achieved.
Presenter's Schedule (faculty access only)
For further details regarding this seminar, please contact Prof. Joyee Deb (email@example.com).
Fall 2023 Microeconomics Theory Seminar Series