Random Priority Research Articles

Expectations-Based Loss Aversion May Help Explain Seemingly Dominated Choices in Strategy-Proof Mechanisms

Deferred Acceptance (DA), a widely implemented algorithm, is meant to improve allocations: under classical preferences, it induces preference-concordant rankings. However, recent evidence shows that—in both real, large-stakes applications and experiments—participants frequently play seemingly dominated, significantly costly, strategies that avoid small chances of good outcomes. We show theoretically why, with expectations-based loss aversion, this behavior may be partly intentional. Reanalyzing existing experimental data on random serial dictatorship (a restriction of DA), we show that such reference-dependent preferences, with a degree and distribution of loss aversion that explain common levels of risk aversion elsewhere, fit the data better than no-loss-aversion preferences. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

RAM: A collection of mechanisms for (indivisible) resource allocation in oTree

The growing theoretical literature on mechanism design and especially on the allocation of indivisible resources has created the need for experimental testing of mechanisms that evolved from matching theory in order to investigate the mechanisms’ theoretical properties in practice. The collection of mechanisms offered by this package includes Deferred Acceptance, Gale’s Top Trading Cycles and the Boston Mechanism in the context of School Choice Problems and the University of Michigan Bidding System, the Gale–Shapley Pareto-Dominant Market Mechanism, and Random Serial Dictatorship in the context of multi-unit resource allocation. All standalone apps are easy to use, customizable for many purposes, and are implemented in the oTree framework.

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.

Performance analysis of scalable video transmission in machine-type-communication caching network

In this article, different from the traditional Device-to-Device caching wireless cellular networks, we consider the scalable video coding performance in cache-based machine-type communication network, where popular videos encoded by scalable video coding method can be cached at machine-type devices with limited memory space. We conduct a comprehensive analysis of the caching hit probability using stochastic geometry, which measures the probability of requested video files cached by nearby local devices and the user satisfaction index, which is essential to delay sensitive video streams. Simulation results prove the derivation of the performance metrics to be correct, using Random cache method and Popularity Priority cache method. It is also demonstrated that scalable video coding–based caching method can be applied according to different user requirements as well as video-type requests, to achieve a better performance.

The Crawler: Two Equivalence Results for Object (Re)Allocation Problems When Preferences are Single-Peaked

For object reallocation problems, if preferences are strict but otherwise unrestricted, the Top Trading Cycle rule (TTC) is the leading rule: It is the only rule satisfying efficiency, the endowment lower bound, and strategy-proofness; moreover, TTC coincides with the core. However, on the subdomain of single-peaked preferences, Bade (2019a) defines a new rule, the “crawler”, which also satisfies the first three properties. Our first theorem states that the crawler and a naturally defined “dual” rule are actually the same. Next, for object allocation problems, we define a probabilistic version of the crawler by choosing an endowment profile at random according to a uniform distribution, and applying the original definition. Our second theorem states that this rule is the same as the “random priority rule” which, as proved by Knuth (1996) and Abdulkadiroglu and Sonmez (1998), is equivalent to the “core from random endowments”.

Efficient and fair assignment mechanisms are strongly group manipulable

We study the assignment of indivisible objects to agents without using monetary transfers. We prove that, regardless of whether the number of objects is sufficient, a mechanism that satisfies ex-post Pareto efficiency, equal treatment of equals, equal total assignment (ETA), and uniform-head fairness (UHF) must be strongly manipulable by a group of agents. In other words, by misreporting their preferences, all group members can obtain lotteries that strictly first-order stochastically dominate the lotteries they would have obtained by reporting their true preferences. ETA requires that agents obtain equal total probability shares of objects. UHF requires that if all agents have equal preferences over a subset of objects and prefer the objects in that subset to the remaining objects, then they obtain equal probability shares of the objects in that subset. The random priority and probabilistic serial mechanisms satisfy our axioms.

Strategy-Proofness of Stochastic Assignment Mechanisms

This paper compares two prominent stochastic assignment mechanisms in the laboratory: Random serial dictatorship (RSD) and top trading cycles with random endowments (TTC). In standard theory, both mechanisms are strategy-proof and Pareto-efficient for the house allocation problem without endowments. In the experiment, RSD outperforms TTC. This can be attributed to more dominant strategy play under RSD. The behavioral theory of obvious strategy-proofness can partly explain this difference in dominant strategy play. Generally, subjects with extremely high and low levels of contingent reasoning play their dominant strategies. These results suggest that one strategy-proof mechanism may outperform another one if individuals are boundedly rational.

Strategy-Proofness of Stochastic Assignment Mechanisms

This paper seeks to identify which algorithm to employ in a situation where goods are distributed to individuals without using money, while treating everyone equally and respecting each individual's preferences. I compare two stochastic assignment mechanisms: Random serial dictatorship (RSD) and top trading cycles with random endowments (TTC). In standard theory, both algorithms are strategy-proof and yield the optimal result. In the experiment, RSD outperforms TTC. This can be attributed to a more dominant strategy play under RSD. Generally, subjects with extremely high and low levels of contingent reasoning play their dominant strategies. These results suggest that one optimal algorithm may outperform another one if individuals are boundedly rational.

The Generalized Random Priority Mechanism with Budgets

This paper studies allocation problems with and without monetary transfers, such as combinatorial auctions, school choice, and course allocation. Interdependent values and multidimensional signals are allowed. Despite known negative results, a mechanism exists that is feasible, ex post individually rational, ex post incentive compatible, and asymptotically both efficient and envy-free. This mechanism is a special case of the generalized random priority mechanism (GRP), which always satisfies the first three properties. The asymptotic properties follow as a corollary of the main theorem: GRP approximates virtually any infinite-market mechanism in large finite markets.

The generalized random priority mechanism with budgets

This paper studies allocation problems with and without monetary transfers, such as combinatorial auctions, school choice, and course allocation. Interdependent values and multidimensional signals are allowed. Despite known negative results, a mechanism exists that is feasible, ex post individually rational, ex post incentive compatible, and asymptotically both efficient and envy-free. This mechanism is a special case of the generalized random priority mechanism (GRP), which always satisfies the first three properties. The asymptotic properties follow as a corollary of the main theorem: GRP approximates virtually any infinite-market mechanism in large finite markets.

Investigating the characteristics of one-sided matching mechanisms under various preferences and risk attitudes

One-sided matching mechanisms are fundamental for assigning a set of indivisible objects to a set of self-interested agents when monetary transfers are not allowed. Two widely-studied randomized mechanisms in multiagent settings are the Random Serial Dictatorship (RSD) and the Probabilistic Serial Rule (PS). Both mechanisms require only that agents specify ordinal preferences and have a number of desirable economic and computational properties. However, the induced outcomes of the mechanisms are often incomparable and thus there are challenges when it comes to deciding which mechanism to adopt in practice. In this paper, we first consider the space of general ordinal preferences and provide empirical results on the (in)comparability of RSD and PS. We analyze their respective economic properties under general and lexicographic preferences. We then instantiate utility functions with the goal of gaining insights on the manipulability, efficiency, and envyfreeness of the mechanisms under different risk-attitude models. Our results hold under various preference distribution models, which further confirm the broad use of RSD in most practical applications.

The object allocation problem with random priorities

The existing priority-based object allocation literature restricts objects' priorities to be deterministic. However, agents might be probabilistically prioritized ex-ante, for instance, through a non-uniform tie-breaking rule. This paper generalizes the deterministic setting by allowing priorities to be random. In this probabilistic environment, we first introduce a fairness notion called claimwise stability in the spirit of the usual stability of Gale and Shapley (1962). We show that the natural generalization of the deferred acceptance mechanism (Gale and Shapley, 1962), so called probabilistic deferred acceptance mechanism, is claimwise stable, but with the downside that it is stochastically dominated by another claimwise stable rule. We then introduce a new mechanism called the constrained probabilistic serial, which is built on the probabilistic serial mechanism of Bogomolnaia and Moulin (2001). It is both claimwise stable and constrained sd-efficient. The paper then systematically compares the probabilistic deferred acceptance and constrained probabilistic serial mechanisms in terms of their strategic and fairness properties.

Probabilistic assignment: an extension approach

We study the problem of allocating objects using lotteries when agents only submit preferences over objects. A standard approach is to “extend” agents’ preferences over objects to preferences over lotteries, using (first-order) stochastic dominance, or the sd-extension. Following (Cho, Games Econ Behav 95:168–177, 2016a), we complement this approach with two alternative extensions, the dl- and ul- extensions, that give rise to lexicographic preferences (dl stands for “downward lexicographic” and ul for “upward lexicographic”) and apply all three of them in tandem to probabilistic assignment. Each property of rules now has three versions that vary with the extension chosen. We introduce a family of rules that generalizes the probabilistic serial rule. Then we study their behavior, as well as that of the random priority rule, in terms of efficiency, no-envy, and strategy-proofness.

Second-best mechanisms in queuing problems without transfers:The role of random priorities

This paper characterizes the second-best mechanism chosen by a benevolent planner under incentive compatibility constraints in queuing problems without monetary transfers. In the absence of monetary compensations, separation between types can only occur if jobs are processed with a probability strictly smaller than one for some configurations of the types. This entails a large efficiency cost, and the planner optimally chooses a pooling contract when types are drawn from a continuous distribution and when binary types are sufficiently close. In the binary model, a separating contract is optimal when the difference between high and low types is large, and results in a low probability of processing jobs when both agents announce high types.

A preference-based, multi-unit auction for pricing and capacity allocation

We study a pricing and allocation problem of a seller of multiple units of a homogeneous item, and present a semi-market mechanism in the form of an iterative ascending-bid auction. The auction elicits buyers’ preferences over a set of options offered by the seller, and processes them with a random-priority assignment scheme to address buyers’ “fairness” expectations. The auction’s termination criterion is derived from a mixed-integer programming formulation of the preference-based capacity allocation problem. We show that the random priority- and preference-based assignment policy is a universally truthful mechanism which can also achieve a Pareto-efficient Nash equilibrium. Computational results demonstrate that the auction mechanism can extract a substantial portion of the centralized system’s profit, indicating its effectiveness for a seller who needs to operate under the “fairness” constraint.

Penjadwalan Job Shop Dengan Pendekatan Algoritma Artificial Immune System

Production scheduling is an important activity in manufacturing. Optimal scheduling affects the time of completion of the work. PT. Interpack is a company that produces packaging machines. The job schedule of the product spare part still uses the random priority rules. Use of random rules makes a lot of time delay. Delay causes operator and machine idle. Delay also causes the total time of completion of the work (makespan) and delay the greater. So it needs to be rescheduled to work on the spare part of product. Job scheduling using the Artificial Immune System (AIS) algorithm. AIS was developed by Farmer et al. The AIS algorithm refers to the human immune system. The stages of the AIS algorithm begin with random initialization, antibody representation and gene classification, clone breeding, selection of donor antibodies, germ-line construction, gene fragment redesign, and ending with diversification of antibodies. AIS algorithm scheduling resulted in a more optimal new schedule. AIS algorithm scheduling generates a future of 6483.91 minutes. Company scheduling generates makespan of 7059.99 minutes. AIS Schedule finishes algorithm 4 days of the due date. AIS algorithm schedule increase machine utility by 1%.

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).

Self-Regulation of an Unobservable Queue

We consider an unobservable M/M/1 queue where customers are homogeneous with respect to service valuation and cost per unit time of waiting. It is well known that left to themselves, in equilibrium, customers join the queue at a rate higher than is socially optimal. Hence, regulation schemes, under which the resulting equilibrium joining rate coincides with the socially optimal one, should be considered. We suggest a classification of regulation schemes based on a few desired properties and use it to classify schemes from the existing literature. To the best of our knowledge, none of the existing schemes possesses all of the properties, and in this paper we suggest such a scheme. Its novelty is in assigning random priorities to customers, prior to their decision whether to join or balk. We also introduce variations of this regulation scheme as well as others that are also based on randomization. The e-companion is available at https://doi.org/10.1287/mnsc.2017.2728 . This paper was accepted by Gad Allon, operations management.

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.