Incentives in One-Sided Matching Problems With Ordinal Preferences

One of the core problems in multiagent systems is how to efficiently allocate a set of indivisible resources to a group of self-interested agents that compete over scarce and limited alternatives. In these settings, mechanism design approaches such as matching mechanisms and auctions are often applied to guarantee fairness and efficiency while preventing agents from manipulating the outcomes. In many multiagent resource allocation problems, the use of monetary transfers or explicit markets are forbidden because of ethical or legal issues. One-sided matching mechanisms exploit various randomization and algorithmic techniques to satisfy certain desirable properties, while incentivizing self-interested agents to report their private preferences truthfully. In the first part of this thesis, we focus on deterministic and randomized matching mechanisms in one-shot settings. We investigate the class of deterministic matching mechanisms when there is a quota to be fulfilled. Building on past results in artificial intelligence and economics, we show that when preferences are lexicographic, serial dictatorship mechanisms (and their sequential dictatorship counterparts) characterize the set of all possible matching mechanisms with desirable economic properties, enabling social planners to remedy the inherent unfairness in deterministic allocation mechanisms by assigning quotas according to some fairness criteria (such as seniority or priority). Extending the quota mechanisms to randomized settings, we show that this class of mechanisms are envyfree, strategyproof, and ex post efficient for any number of agents and objects and any quota system, proving that the well-studied Random Serial Dictatorship (RSD) is also envyfree in this domain. The next contribution of this thesis is providing a systemic empirical study of the two widely adopted randomized mechanisms, namely Random Serial Dictatorship (RSD) and the Probabilistic Serial Rule (PS). We investigate various properties of these two mechanisms such as efficiency, strategyproofness, and envyfreeness under various preference assumptions (e.g. general ordinal preferences, lexicographic preferences, and risk attitudes). The empirical findings in this thesis complement the theoretical guarantees of matching mechanisms, shedding light on practical implications of deploying each of the given mechanisms. In the second part of this thesis, we address the issues of designing truthful matching mechanisms in dynamic settings. Many multiagent domains require reasoning over time and are inherently dynamic rather than static. We initiate the study of matching problems where agents’ private preferences evolve stochastically over time, and decisions have to be made in each period. To adequately evaluate the quality of outcomes in dynamic settings,