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

Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms

The random priority (random serial dictatorship) mechanism is a common method for assigning objects to individuals. The mechanism is easy to implement and strategy-proof. However this mechanism is inefficient, as the agents may be made all better off by another mechanism that increases their chances of obtaining more preferred objects. Such an inefficiency is eliminated by the recent mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications has been an open question. This paper shows that these mechanisms become equivalent when the market becomes large. More specifically, given a set of object types, the random assignments in these mechanisms converge to each other as the number of copies of each object type approaches infinity. Thus, the inefficiency of the random priority mechanism becomes small in large markets. Our result gives some rationale for the common use of the random priority mechanism in practical problems such as student placement in public schools.Random assignment, Random priority, Probabilistic serial, Ordinal efficiency, Asymptotic equivalence

Size versus fairness in the assignment problem

When not all objects are acceptable to all agents, maximizing the number of objects actually assigned is an important design concern. We compute the guaranteed size ratio of the Probabilistic Serial mechanism, i.e., the worst ratio of the actual expected size to the maximal feasible size. It converges decreasingly to 1 − 1 e 63.2% as the maximal size increases. It is the best ratio of any Envy-Free assignment mechanism

Aggregate efficiency in random assignment problems

We introduce aggregate efficiency (AE) for random assignments (RA) by requiring higher expected numbers of agents be assigned to their more preferred choices. It is shown that the realizations of any aggregate efficient random assignment (AERA) must be an AE permutation matrix. While AE implies ordinally efficiency, the reverse does not hold. And there is no mechanism treating equals equally while satisfying weak strategyproofness and AE. But, a new mechanism, the reservation-1 (R1), is identified and shown to provide an improvement on grounds of AE over the probabilistic serial mechanism of Bogomolnaia and Moulin (2001). We prove that R1 is weakly strategyproof, ordinally efficient, and weak envy--free. Moreover, the characterization of R1 displays that it is the probabilistic serial mechanism updated by a principle decreed by the Turkish parliament concerning the random assignment of new doctors: Modifying the axioms of Hasimoto, et. al. (2012) characterizing the probabilistic serial mechanism to satisfy this principle, fully characterizes R1

I don't want to miss a thing : learning dynamics and effects of feedback type and monetary incentive in a paired associate deterministic learning task

Effective functioning in a complex environment requires adjusting of behavior according to changing situational demands. To do so, organisms must learn new, more adaptive behaviors by extracting the necessary information from externally provided feedback. Not surprisingly, feedback-guided learning has been extensively studied using multiple research paradigms. The purpose of the present study was to test the newly designed Paired Associate Deterministic Learning task (PADL), in which participants were presented with either positive or negative deterministic feedback. Moreover, we manipulated the level of motivation in the learning process by comparing blocks with strictly cognitive, informative feedback to blocks where participants were additionally motivated by anticipated monetary reward or loss. Our results proved the PADL to be a useful tool not only for studying the learning process in a deterministic environment, but also, due to the varying task conditions, for assessing differences in learning patterns. Particularly, we show that the learning process itself is influenced by manipulating both the type of feedback information and the motivational significance associated with the expected monetary reward

The UN in the lab

We consider two alternatives to inaction for governments combating terrorism, which we term Defense and Prevention. Defense consists of investing in resources that reduce the impact of an attack, and generates a negative externality to other governments, making their countries a more attractive objective for terrorists. In contrast, Prevention, which consists of investing in resources that reduce the ability of the terrorist organization to mount an attack, creates a positive externality by reducing the overall threat of terrorism for all. This interaction is captured using a simple 3×3 “Nested Prisoner’s Dilemma” game, with a single Nash equilibrium where both countries choose Defense. Due to the structure of this interaction, countries can benefit from coordination of policy choices, and international institutions (such as the UN) can be utilized to facilitate coordination by implementing agreements to share the burden of Prevention. We introduce an institution that implements a burden-sharing policy for Prevention, and investigate experimentally whether subjects coordinate on a cooperative strategy more frequently under different levels of cost sharing. In all treatments, burden sharing leaves the Prisoner’s Dilemma structure and Nash equilibrium of the game unchanged. We compare three levels of burden sharing to a baseline in a between-subjects design, and find that burden sharing generates a non-linear effect on the choice of the efficient Prevention strategy and overall performance. Only an institution supporting a high level of mandatory burden sharing generates a significant improvement in the use of the Prevention strategy

The Mechanism Design Approach to Student Assignment

The mechanism design approach to student assignment involves the theoretical, empirical, and experimental study of systems used to allocate students into schools around the world. Recent practical experience designing systems for student assignment has raised new theoretical questions for the theory of matching and assignment. This article reviews some of this recent literature, highlighting how issues from the field motivated theoretical developments and emphasizing how the dialogue may be a road map for other areas of applied mechanism design. Finally, it concludes with some open questions.National Science Foundation (U.S.