Strategy-proof and Efficient Fair Scheduling

In this paper, I study dynamic and sequential fair division problems for players with dichotomous preferences and devise a systematic approach of designing efficient, envy-free, and strategy-proof mechanisms for any generic problem. The mechanisms developed here can accommodate common discount factors to represent players’ time preferences between different periods. I also show that the mechanisms proposed in the current research outperform in efficiency the repeated applications of a static strategy-proof mechanism by a factor of the size of set of players in refined problems with unbounded demands. I also contribute a novel comparative statics result on the egalitarian solutions to monotone and concave cooperative games with transferable utilities in characteristic function form. In the process of doing so, I discover a duality-like property of the egalitarian solutions and reconcile the seemingly contradictory process to the objective in the search for them. Finally, I highlight the relative importance of identifying the correct order of priority over choices of payoffs in the pursuit of equality.