Equilibria Under the Probabilistic Serial Rule

The probabilistic serial (PS) rule is a prominent randomized rule for assigning indivisible goods to agents. Although it is well known for its good fairness and welfare properties, it is not strategyproof. In view of this, we address several fundamental questions regarding equilibria under PS. Firstly, we show that Nash deviations under the PS rule can cycle. Despite the possibilities of cycles, we prove that a pure Nash equilibrium is guaranteed to exist under the PS rule. We then show that verifying whether a given profile is a pure Nash equilibrium is coNP-complete, and computing a pure Nash equilibrium is NP-hard. For two agents, we present a linear-time algorithm to compute a pure Nash equilibrium which yields the same assignment as the truthful profile. Finally, we conduct experiments to evaluate the quality of the equilibria that exist under the PS rule, finding that the vast majority of pure Nash equilibria yield social welfare that is at least that of the truthful profile.Comment: arXiv admin note: text overlap with arXiv:1401.6523, this paper supersedes the equilibria section in our previous report arXiv:1401.652

Equilibria in Sequential Allocation

Sequential allocation is a simple mechanism for sharing multiple indivisible items. We study strategic behavior in sequential allocation. In particular, we consider Nash dynamics, as well as the computation and Pareto optimality of pure equilibria, and Stackelberg strategies. We first demonstrate that, even for two agents, better responses can cycle. We then present a linear-time algorithm that returns a profile (which we call the "bluff profile") that is in pure Nash equilibrium. Interestingly, the outcome of the bluff profile is the same as that of the truthful profile and the profile is in pure Nash equilibrium for \emph{all} cardinal utilities consistent with the ordinal preferences. We show that the outcome of the bluff profile is Pareto optimal with respect to pairwise comparisons. In contrast, we show that an assignment may not be Pareto optimal with respect to pairwise comparisons even if it is a result of a preference profile that is in pure Nash equilibrium for all utilities consistent with ordinal preferences. Finally, we present a dynamic program to compute an optimal Stackelberg strategy for two agents, where the second agent has a constant number of distinct values for the items

Social Welfare in One-Sided Matching Mechanisms

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of $\Omega(\sqrt{n})$ on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms

Allocation of Divisible Goods under Lexicographic Preferences

We present a simple and natural non-pricing mechanism for allocating divisible goods among strategic agents having lexicographic preferences. Our mechanism has favorable properties of incentive compatibility (strategy-proofness), Pareto efficiency, envy-freeness, and time efficiency

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

Controlling the Fairness / Accuracy Tradeoff in Recommender Systems

Recommender systems are one of the most pervasive applications of machine learning. They play a pivotal role in helping users find items tailored to their taste. Although these systems intend to assist people in their information needs, they can cause implicit or explicit discrimination against individuals or groups. There are several ways that different biases can creep into recommender systems. Reflection of societal and historical prejudices in datasets and during the data collection process, lack of sufficient data on minority groups, lack of suitable evaluation methods and model designs to detect these biases and lessen the unfairness caused by them are among the many reasons for unfairness in these systems. A system needs to defend against the biases in recommendation output to prevent harm and unfairness. However, integrating the goal of fairness with accuracy in recommender systems is challenging, primarily because of this goal's significant trade-offs with accuracy. Accuracy in recommender systems is the ability of that system to predict users' needs and interests accurately. On the other hand, fairness is a complicated concept with a variety of definitions. To use fairness as an objective, we need to define it based on the application area and the context of a problem. Additionally, we need to specify the fairness concerns of the different stakeholders involved in the recommender systems and the fairness priorities of a system. Any of these aspects might disagree with the goal of accuracy. For example, if fairness for content providers is more exposure to users, increasing it might cause a reduction in accuracy. Therefore, controlling the trade-off between accuracy and fairness becomes essential. Throughout this dissertation, several recommendation models and re-ranking approaches are presented that aim to address this problem using in- and post- processing methods. These approaches show promising results, but it is worth mentioning that they have intrinsic limitations and, therefore, shouldn't be considered ultimate solutions