Essays in mechanism design

The Gibbard-Satterthwaite Theorem (Gibbard, 1973, Satterthwaite, 1975) states that when there is no restriction on admissible preferences, only dictatorial rules satisfy strategy-proofness (no one can ever be better off by lying about his preference) and “the full range condition”. The unrestricted domain assumption, however, does not hold in most economic environments of interest. The main objective of this thesis is to investigate the possibility of designing strategy-proof rules in such restricted environments.; In Chapter 2, we study 2-agent exchange economies. We identify general properties of preference domains and show that given any domain satisfying these properties, dictatorial rules are the only efficient and strategy-proof rules.; In Chapter 3, we extend the impossibility result for the 2-agent case to the n-agent case by imposing the additional requirement of continuity.; In Chapter 4, we consider “risk sharing problems” specified by a common prior and expected utility preferences over a state-contingent commodity space. When aggregate certainty holds, we show that every selection from the Walrasian correspondence is efficient, individually rational , and strategy-proof. Moreover, we show that the converse also holds. However, when aggregate uncertainty holds, we show that in the 2-agent case, dictatorial rules are the only efficient and strategy-proof rules.; In Chapters 5, 6 and 7, we consider the problem of choosing a subset of a set of indivisible objects (public projects, facilities, laws, etc.), when preferences are “separable”.; In Chapter 5, we characterize strategy-proof “voting rules” satisfying several combinations of the following axioms: null-independence, efficiency, voter sovereignty, anonymity, and neutrality.; In Chapter 6, we study the manipulability of voting rules in an environment where voters may lie about their preferences or misrepresent the agenda (a set of proposals) by dividing it into subagendas or replacing some positive proposals with their negative counterparts or conversely. Among anonymous and neutral voting rules, we characterize the class of minimally manipulable rules.; In Chapter 7, we study non-manipulability in conjunction with a notion of “restricted efficiency” and anonymity . We show that there exist a unique class of rules that minimally violate anonymity within voting rules satisfying restricted efficiency and non-manipulability.