Bounded incentives in manipulating the probabilistic serial rule

The Probabilistic Serial mechanism is valued for its fairness and efficiency in addressing the random assignment problem. However, it lacks truthfulness, meaning it works well only when agents' stated preferences match their true ones. Significant utility gains from strategic actions may lead self-interested agents to manipulate the mechanism, undermining its practical adoption. To gauge the potential for manipulation, we explore an extreme scenario where a manipulator has complete knowledge of other agents' reports and unlimited computational resources to find their best strategy. We establish tight incentive ratio bounds of the mechanism. Furthermore, we complement these worst-case guarantees by conducting experiments to assess an agent's average utility gain through manipulation. The findings reveal that the incentive for manipulation is very small. These results offer insights into the mechanism's resilience against strategic manipulation, moving beyond the recognition of its lack of incentive compatibility

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

An equilibrium analysis of the probabilistic serial mechanism

Due to copyright restrictions, the access to the full text of this article is only available via subscription.The prominent mechanism of the recent literature in the assignment problem is the probabilistic serial (PS). Under PS, the truthful (preference) proÖle always constitutes an ordinal Nash Equilibrium, inducing a random assignment that satisÖes the appealing ordinal e¢ ciency and envy-freeness properties. We show that both properties may fail to be satisÖed by a random assignment induced in an ordinal Nash Equilibrium where one or more agents are non-truthful. Worse still, the truthful proÖle may not constitute a Nash Equilibrium, and every non-truthful proÖle that constitutes a Nash Equilibrium may lead to a random assignment which is not ordinally e¢ cient, not even weakly envy-free, and which admits an ex-post ine¢ cient decomposition. A strong ordinal Nash Equilibrium may not exist, but when it exists, any proÖle that constitutes a strong ordinal Nash Equilibrium induces the random assignment induced under the truthful proÖle. The results of our equilibrium analysis of PS call for caution when implementing it in small assignment problems