Social Welfare in Algorithmic Mechanism Design Without Money

Social choice theory is concerned with collective decision making under different, possibly contrasting opinions and has been part of the core of society since ancient times. The goal is to implement some socially desired objective while at the same time accounting for the fact that people will act strategically, in order to manipulate the outcomes in their favor. In this thesis, we consider the well-known objective of social welfare, i.e. the sum of individual utilities as the social objective and following the agenda of algorithmic mechanism design, we study how well our objectives can be approximated by mechanisms that prevent or predict the effects of the agents’ strategic nature. We adopt two approaches; on one hand, we study truthful mechanisms and bound their approximation ratios and on the other hand, we study the effect of strategic play on non-truthful mechanisms, by bounding their price of anarchy. Our results provide worst-case guarantees for the performance of mechanisms in voting scenarios and resource allocation problems. In the first part of the thesis, we consider the general social choice setting, where agents have unrestricted cardinal preferences over a finite set of outcomes and we study the capabilities and limitations of truthful mechanisms for the social welfare objective. We prove upper and lower bounds on the approximation ratio of natural classes of mechanisms, as well as the class of all mechanisms. In the second part, we bound the inefficiency of mechanisms for the one-sided matching problem. We study both truthful and non-truthful mechanisms and prove that some very well-known mechanisms in literature are asymptotically optimal among all mechanisms. Finally, in the last part of the thesis, we study social welfare maximization for the problem of allocating divisible items among agents and bound the price of anarchy of the Fisher market mechanism, a mechanism based on a fundamental market model.