No-envy and dominant strategy implementability in non-excludable public good economies with quasi-linear preferences

This paper studies the relationship between no-envy (Foley, D. (1967) "Resource allocation and the public sector," Yale Economics Essays 7, pp.45-98) and dominant strategy implementability in non-excludable public good economies with quasi-linear preferences. The main result shows that the combination of non-bossiness (Satterthwaite, M. A. and H. Sonnenschein (1981) "Strategy-proof allocation mechanisms at differentiable points," Review of Economic Studies 48, pp.587-597) and equal treatment of equals is equivalent to no-envy under strategy-proof social choice functions in the economies which are incompatible with strict monotonic closedness (Fleurbaey, M. and F. Maniquet (1997) "Implementability and horizontal equity imply no-envy," Econometrica 65, pp.1215-1219).