Random Serial Dictatorship Mechanism Research Articles

Inefficiency of Random Serial Dictatorship under incomplete information

We study the problem of allocating n objects to n agents without monetary transfers in a setting where each agent's preference over objects is private. We assume that each agent's value vector (values for n objects) is independently drawn from an exchangeable distribution and show that the celebrated Random Serial Dictatorship mechanism is welfare inferior to another allocation method, the Random Boston mechanism, when the number of agents and objects is large. Specifically, every type of every agent has a strictly higher interim expected utility under the Random Boston mechanism than under the Random Serial Dictatorship mechanism. Moreover, this strict dominance holds even at the limit.

A planner-optimal matching mechanism and its incentive compatibility in a restricted domain

In many random assignment problems, the central planner pursues their own policy objective, such as matching size and minimum quota fulfillment. Several practically important policy objectives do not align with agents' preferences and are known to be incompatible with strategy-proofness. This paper demonstrates that such policy objectives can be attained using mechanisms that satisfy Bayesian incentive compatibility within a restricted domain of von Neumann Morgenstern utilities. We establish that a mechanism satisfies Bayesian incentive compatibility in an inverse-bounded-indifference domain if and only if the mechanism satisfies the three axioms of swap monotonicity, lower invariance, and interior upper variance. We apply this axiomatic characterization to analyze the incentive property of the constrained random serial dictatorship mechanism (CRSD). CRSD is designed to generate an individually rational assignment that optimizes the central planner's policy objective function. Since CRSD satisfies these axioms, it is Bayesian incentive compatible within an IBI domain.

Strategic experimentation with random serial dictatorship

We consider matching-mechanism design in an environment in which agents acquire information about their preferences endogenously. Information is costly; thus, agents acquire information only if it is relevant to their decision-making. Agents' beliefs about their choice set (i.e., the set of objects each agent can obtain) are therefore crucial for incentives in information acquisition. This study demonstrates that the implementation of matching mechanisms changes the equilibrium consequence because it influences agents' beliefs about choice sets. We analyze the behavior of the random serial dictatorship mechanism in a stylized environment. We construct a family of economies in which agents have independent and private values but information disclosure about choice sets leads to inefficient outcome. We induce more efficient information acquisition through information design.

Size versus truncation robustness in the assignment problem

We study the size of matchings (expected number of agents matched to some objects) generated by random mechanisms in the assignment problem. We show that no mechanism that satisfies two weak axioms, weak truncation robustness and weak regularity, achieves an approximation ratio better than 1−1∕e≈63.2%. This result indicates that it is impossible to achieve a matching size larger than 63.2% of the maximum feasible size in the worst case, as long as agents’ preferences over objects are private information. Our result indicates that the random serial dictatorship mechanism and probabilistic serial mechanism (which indeed has an approximation ratio of 1−1∕e) have the best approximation ratio among a broad class of mechanisms.

Size Versus Truthfulness in the House Allocation Problem

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomised mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomised mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of frac{e}{e-1}. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of frac{18}{13} on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. By using a characterisation result of Bade, we show that any randomised mechanism that is a symmetrisation of a truthful, non-bossy and Pareto optimal mechanism has an improved lower bound of frac{e}{e-1}. Since our new mechanism is a symmetrisation of RSDM for strict preferences, it follows that this lower bound is tight. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomised strategy of the administrator who interviews the applicants.

Size versus Truncation Robustness in the Assignment Problem

We study the size of matchings (expected number of agents matched to some objects) generated by random mechanisms in the assignment problem. We show that no mechanism that satisfies two weak axioms, weak truncation robustness and weak regularity, achieves an approximation ratio better than 1 - 1/e = 63.2%. This result indicates that it is impossible to achieve a matching size larger than 63.2% of the maximum feasible size in the worst case, as long as agents' preferences over objects are private information. Our result indicates that the random serial dictatorship mechanism and probabilistic serial mechanism (which indeed has an approximation ratio of 1 - 1/e) have the best approximation ratio among a broad class of mechanisms.

Fairness and efficiency in strategy-proof object allocation mechanisms

I consider the problem of allocating N indivisible objects among N agents according to their preferences when transfers are absent and an outside option may exist. I study the tradeoff between fairness and efficiency in the class of strategy-proof mechanisms. The main finding is that for strategy-proof mechanisms the following efficiency and fairness criteria are mutually incompatible: (1) ex-post efficiency and envy-freeness, (2) ordinal efficiency and weak envy-freeness, and (3) ordinal efficiency and equal division lower bound. Result 1 is the first impossibility result for this setting that uses ex-post efficiency; results 2 and 3 are more practical than similar results in the literature. In addition, for N=3, I give two characterizations of the celebrated random serial dictatorship mechanism: it is the unique strategy-proof, ex-post efficient mechanism that (4) provides agents that have the same ordinal preferences with assignments not dominated by each other (weak envy-freeness among equals), or (5) provides agents that have the same cardinal preferences with assignments of equal expected utility (symmetry). These results strengthen the characterization by Bogomolnaia and Moulin (2001); result 5 implies the impossibility result by Zhou (1990).

Strategic Experimentation with Random Serial Dictatorship

We consider matching-mechanism design in an environment in which agents acquire information about their preferences endogenously. Information is costly; thus, agents acquire information only if it is relevant to their decision-making. Agents' beliefs about their choice set (i.e., the set of objects each agent can obtain) are therefore crucial for incentives in information acquisition. This study demonstrates that the implementation of matching mechanisms changes the equilibrium consequence because it influences agents' beliefs about choice sets. We analyze the behavior of the random serial dictatorship mechanism in a stylized environment. We show that the full-disclosure policy (which corresponds to sequential implementation) is typically Pareto inefficient because it fails to exploit the positive externality of information acquisition. We induce more efficient information acquisition through information design.

Efficient lottery design

There has been a surge of interest in stochastic assignment mechanisms that have proven to be theoretically compelling thanks to their prominent welfare properties. Contrary to stochastic mechanisms, however, lottery mechanisms are commonly used in real life for indivisible goods allocation. To help facilitate the design of practical lottery mechanisms, we provide new tools for obtaining stochastic improvements in lotteries. As applications, we propose lottery mechanisms that improve upon the widely used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism. The tools we provide here can be useful in developing welfare-enhanced new lottery mechanisms for practical applications such as school choice.

Strategy-Proof Probabilistic Mechanisms for Public Decision with Money

We study strategy-proof probabilistic mechanisms in a binary public decision model when monetary transfers are allowed. We consider not only the pivotal mechanism, the majority voting mechanism, the random serial dictatorship mechanism, and the unanimity mechanism, but also the random chair pivotal mechanism (Faltings 2005), which is a probabilistic variant of the pivotal mechanism.We first show that the random chair pivotal mechanism, the majority voting mechanism, the random serial dictatorship mechanism, and the unanimity mechanism are second-best efficient.Next, we calculate the expected welfare of the mechanisms by the Monte Carlo method, where each agent's valuation is independently, identically, and uniformly (or normally) distributed. These calculations exhibit that the random chair pivotal mechanism is more efficient than the other mechanisms. We also show that in large economies, the random chair pivotal mechanism is efficient, while the other mechanisms might be highly inefficient.Finally, we characterize the random chair pivotal mechanism with strategy-proofness, budget-balance, equal treatment of equals, and decision-robustness.

On Manipulablity of Random Serial Dictatorship in Sequential Matching with Dynamic Preferences

We consider the problem of repeatedly matching a set of alternatives to a set of agents in the absence of monetary transfer. We propose a generic framework for evaluating sequential matching mechanisms with dynamic preferences, and show that unlike single-shot settings, the random serial dictatorship mechanism is manipulable.

An experimental study on the incentives of the probabilistic serial mechanism

We report an experiment on the Probabilistic Serial (PS) mechanism for allocating indivisible goods. The PS mechanism, a recently discovered alternative to the widely used Random Serial Dictatorship mechanism, has attractive fairness and efficiency properties if people report their preferences truthfully. However, the mechanism is not strategy-proof, so participants may not truthfully report their preferences. We investigate misreporting in a set of simple applications of the PS mechanism. We confront subjects with situations in which the theory suggests that there is an incentive or no incentive to misreport. We find little misreporting in situations where misreporting is a Nash equilibrium. However, we also find a significant degree of misreporting in situations where there is actually no benefit to doing so. These findings suggest that the PS mechanism may have problems in terms of truthful elicitation.

An Experimental Study on the Incentives of the Probabilistic Serial Mechanism

We report an experiment on the Probabilistic Serial (PS) mechanism for allocating indivisible goods. The PS mechanism, a recently discovered alternative to the widely used Random Serial Dictatorship mechanism, has attractive fairness and efficiency properties if people report their preferences truthfully. However, the mechanism is not strategy-proof, so participants may not truthfully report their preferences. We investigate misreporting in a set of simple applications of the PS mechanism. We confront subjects with situations in which theory suggests that there is an incentive or no incentive to misreport. We find little misreporting in situations where misreporting is a Nash equilibrium. However, we also find a significant degree of misreporting in sitations where there is actually no benefit to doing so. These findings suggest that the PS mechanism may have problems in terms of truthful elicitation.