Strategy-Proof and Efficient Fair Scheduling

In this paper, I study dynamic and sequential fair division problems for players with dichotomous preferences. I have devised a systematic approach of designing efficient, envy-free, and strategy-proof mechanisms for generic problems. The mechanisms developed in this paper 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 number of players in refined problems with unbounded demands. I 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, I have discovered a duality-like property of the egalitarian solutions and reconciled the seemingly contradictory proceedings to the goal of searching for the egalitarian solutions. Finally, I highlight the relative importance of identifying the correct order of priority over choices of payoffs in the pursuit of equality