Random assignments with uniform preferences: An impossibility result

Agents have uniform preferences if a weakly decreasing utility function determines each agent's preference ranking over the same order of alternatives. We show that the impossibility in the random assignment problem between strategyproofness, ordinally efficiency, and fairness in the sense of equal division lower bound, prevails even if agents have uniform preferences. Furthermore, it continues to hold even if we weaken the strategyproofness to upper-contour strategyproofness, or the ordinal efficiency to robust ex-post Pareto efficiency

The Pareto Frontier for Random Mechanisms

We study the trade-offs between strategyproofness and other desiderata, such as efficiency or fairness, that often arise in the design of random ordinal mechanisms. We use approximate strategyproofness to define manipulability, a measure to quantify the incentive properties of non-strategyproof mechanisms, and we introduce the deficit, a measure to quantify the performance of mechanisms with respect to another desideratum. When this desideratum is incompatible with strategyproofness, mechanisms that trade off manipulability and deficit optimally form the Pareto frontier. Our main contribution is a structural characterization of this Pareto frontier, and we present algorithms that exploit this structure to compute it. To illustrate its shape, we apply our results for two different desiderata, namely Plurality and Veto scoring, in settings with 3 alternatives and up to 18 agents.Comment: Working Pape

Partial Strategyproofness: Relaxing Strategyproofness for the Random Assignment Problem

We present partial strategyproofness, a new, relaxed notion of strategyproofness for studying the incentive properties of non-strategyproof assignment mechanisms. Informally, a mechanism is partially strategyproof if it makes truthful reporting a dominant strategy for those agents whose preference intensities differ sufficiently between any two objects. We demonstrate that partial strategyproofness is axiomatically motivated and yields a parametric measure for "how strategyproof" an assignment mechanism is. We apply this new concept to derive novel insights about the incentive properties of the probabilistic serial mechanism and different variants of the Boston mechanism.Comment: Working Pape

House allocation with fractional endowments

This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extend to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain

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, we propose a generic stochastic decision process and show that, in contrast to static settings, traditional mechanisms are easily manipulable. We introduce a number of properties that we argue are important for matching mechanisms in dynamic settings and propose a new mechanism that maintains a history of pairwise interactions between agents, and adapts the priority orderings of agents in each period based on this history. We show that our mechanism is globally strategyproof in certain settings (e.g. when there are 2 agents or when the planning horizon is bounded), and even when the mechanism is manipulable, the manipulative actions taken by an agent will often result in a Pareto improvement in general. Thus, we make the argument that while manipulative behavior may still be unavoidable, it is not necessarily at the cost to other agents. To circumvent the issues of incentive design in dynamic settings, we formulate the dynamic matching problem as a Multiagent MDP where agents have particular underlying utility functions (e.g. linear positional utility functions), and show that the impossibility results still exist in this restricted setting. Nevertheless, we introduce a few classes of problems with restricted preference dynamics for which positive results exist. Finally, we propose an algorithmic solution for agents with single-minded preferences that satisfies strategyproofness, Pareto efficiency, and weak non-bossiness in one-shot settings, and show that even though this mechanism is manipulable in dynamic settings, any unilateral deviation would benefit all participating agents

On the Trade-offs between Modeling Power and Algorithmic Complexity

Mathematical modeling is a central component of operations research. Most of the academic research in our field focuses on developing algorithmic tools for solving various mathematical problems arising from our models. However, our procedure for selecting the best model to use in any particular application is ad hoc. This dissertation seeks to rigorously quantify the trade-offs between various design criteria in model construction through a series of case studies. The hope is that a better understanding of the pros and cons of different models (for the same application) can guide and improve the model selection process. In this dissertation, we focus on two broad types of trade-offs. The first type arises naturally in mechanism or market design, a discipline that focuses on developing optimization models for complex multi-agent systems. Such systems may require satisfying multiple objectives that are potentially in conflict with one another. Hence, finding a solution that simultaneously satisfies several design requirements is challenging. The second type addresses the dynamics between model complexity and computational tractability in the context of approximation algorithms for some discrete optimization problems. The need to study this type of trade-offs is motivated by certain industry problems where the goal is to obtain the best solution within a reasonable time frame. Hence, being able to quantify and compare the degree of sub-optimality of the solution obtained under different models is helpful. Chapters 2-5 of the dissertation focus on trade-offs of the first type and Chapters 6-7 the second type