Valuation asymmetry in the dynamic private provision of public goods

I consider a dynamic game of private provision of a discrete public good by individuals who derive asymmetric flow benefits every period upon project completion. The individuals are otherwise homogeneous. I show that an asymmetric Markov perfect equilibrium (MPE) exists, which is either a completion equilibrium (where the good is provided) or a no-contribution equilibrium depending on the benefits asymmetry. A completion equilibrium does not require all the agents to contribute at every period. Along an MPE, an individual contributes from the beginning (t=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0$$\end{document}), irrespective of others' contributions, if her flow benefit exceeds a contribution threshold. Individual contributions are strategic complements across time; however, the coefficient of strategic complementarity is independent of valuation asymmetry. A higher valuation individual makes a larger absolute contribution every period. I show that all the socially beneficial projects get completed in an asymmetric MPE when the higher valuation individual's flow benefit exceeds that contribution threshold and that an asymmetric completion MPE is efficiency improving compared to its symmetric counterpart.