| This dissertation contains my research in the design of division mechanisms for self-interested players with dichotomous preferences. The first chapter studies static division problems and constructs a class of efficient and strategy-proof division mechanisms that accommodate a variety of distributive objectives. In establishing strategy-proof-ness, it provides a comparative statics result on potentially asymmetric Nash collective utility maximizers of monotone and concave cooperative games with transferable utilities. The second chapter studies the comparative statics of egalitarian solutions of monotone and concave cooperative games with transferable utilities and offers a novel result on the interpersonal comparisons between players' payoff changes due to increases in the values of characteristic functions. It also amends previous work by offering definitive proofs to known results only loosely established by other authors before and serves as the backbone of the results in the third chapter. Last but not least, the third chapter devises a systematic way of constructing consistent, efficient, envy-free, and strategy-proof dynamic or sequential division mechanisms for generic division problems with procedural or periodic constraints. These mechanisms possess strong incentive properties for infinite refined problems and outperform repeated equal divisions in efficiency by a factor of the size of the population. |
