This thesis serves as a step toward a better understanding of how to design fair and efficient multiagent resource allocation systems by bringing the incentives of the participating agents to the center of the design process. As the quality of these systems critically depends on the ways in which the participants interact with each other and with the system, an ill-designed set of incentives can lead to severe inefficiencies. The special focus of this work is on the problems that arise when the use of monetary exchanges between the system and the participants is prohibited. This is a common restriction that substantially complicates the designer's task; we nevertheless provide a sequence of positive results in the form of mechanisms that maximize efficiency or fairness despite the possibly self-interested behavior of the participating agents.
The first part of this work is a contribution to the literature on approximate mechanism design without money. Given a set of divisible resources, our goal is to design a mechanism that allocates them among the agents. The main complication here is due to the fact that the agents' preferences over different allocations of these resources may not be known to the system. Therefore, the mechanism needs to be designed in such a way that it is in the best interest of every agent to report the truth about her preferences; since monetary rewards and penalties cannot be used in order to elicit the truth, a much more delicate regulation of the resource allocation is necessary. Our contribution mostly revolves around a new truthful mechanism that we propose, which we call the /Partial Allocation/ mechanism. We first show how to use the two-agent version of this mechanism to create a system with the best currently known worst-case efficiency guarantees for problem instances involving two agents. We then consider fairness measures and prove that the general version of this elegant mechanism yields surprisingly good approximation guarantees for the classic problem of fair division. More specifically, we use the well established solution of /Proportional Fairness/ as a benchmark and we show that for an arbitrary number of agents and resources, and for a very large class of agent preferences, our mechanism provides /every agent/ with a value close to her proportionally fair value. We complement these results by also studying the limits of truthful money-free mechanisms, and by providing other mechanisms for special classes of problem instances. Finally, we uncover interesting connections between our mechanism and the Vickrey-Clarke-Groves mechanism from the literature on mechanism design with money.
The second part of this work concerns the design of money-free resource allocation mechanisms for /decentralized/ multiagent systems. As the world has become increasingly interconnected, such systems are using more and more resources that are geographically dispersed; in order to provide scalability in these systems, the mechanisms need to be decentralized. That is, the allocation decisions for any given resource should not assume global information regarding the system's resources or participants. We approach this restriction by using /coordination mechanisms/: a collection of simple resource allocation policies, each of which controls only one of the resources and uses only local information regarding the state of the system. The system's participants, facing these policies, have the option of choosing which resources they will access. We study a variety of coordination mechanisms and we prove that the social welfare of any equilibrium of the games that these mechanisms induce is a good approximation of the optimal welfare. Once again, we complement our positive results by studying the limits of coordination mechanisms. We also provide a detailed explanation of the seemingly counter-intuitive incentives that some of these mechanisms yield. Finally, we use this understanding in order to design a combinatorial constant-factor approximation algorithm for maximizing the social welfare, thus providing evidence that a game-theoretic mindset can lead to novel optimization algorithms.