Serial dictatorship and Pareto optimality

In a deterministic allocation problem in which each agent is entitled to receive exactly one object, an allocation is Pareto optimal if and only if it is the outcome of a serial dictatorship. We extend the definition of serial dictatorship to settings in which some agents may be entitled to receive more than one object, and study the efficiency and uniqueness properties of the equilibrium allocations. We prove that subgame perfect equilibrium allocations of serial dictatorship games are not necessarily Pareto optimal; and generally not all Pareto optima can be implemented as subgame perfect equilibrium allocations of serial dictatorship games, except in the 2-agent separable preference case. Moreover, serial dictatorship games do not necessarily have unique subgame perfect equilibrium allocations, except in the 2-agent case, hence their outcomes are indeterminate and manipulable.     

Secure implementation in Shapley–Scarf housing markets

This paper considers the object allocation problem introduced by Shapley and Scarf (J Math Econ 1:23–37, 1974). We study secure implementation (Saijo et al. in Theor Econ 2:203–229, 2007), that is, double implementation in dominant strategy and Nash equilibria. We prove that (1) an individually rational solution is securely implementable if and only if it is the no-trade solution, (2) a neutral solution is securely implementable if and only if it is a serial dictatorship, and (3) an efficient solution is securely implementable if and only if it is a sequential dictatorship. Furthermore, we provide a complete characterization of securely implementable solutions in the two-agent case: a solution is securely implementable if and only if it is either a constant solution or a serial dictatorship.     

Non-cooperative bargaining and the incomplete informational core

In an exchange economy with incomplete information, the signaling core is defined by the set of state-contingent allocations to which no coalitions object under informational leakage through proposals by informed agents. An objection underlying the signaling core is supported by a sequential equilibrium of an ultimatum bargaining game with an informed proposer. We prove that a stationary sequential equilibrium allocation in a Rubinstein-type sequential bargaining game with a restart rule belongs to the signaling core if the belief of players satisfies a self-selection property.     

STRATEGY PROOF AND PRIVACY PRESERVING FAIR ALLOCATION MECHANISM*

We study a fair division problem with indivisible objects such as jobs, houses and one divisible good like money. It is required that each agent be assigned with exactly one object and a certain amount of money. Agents are assumed to have quasi‐linear utilities in money but their reservation values over the objects are private information. A dynamic mechanism is proposed that induces all agents to act honestly rather than strategically and assigns the objects with money to agents efficiently and fairly; at the same time it achieves privacy protection for the agents.     

Random dictatorship domains

A domain of preference orderings is a random dictatorship domain if every strategy-proof random social choice function satisfying unanimity defined on the domain is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We ask whether an arbitrary dictatorial domain is a random dictatorship domain and show that the answer is negative by constructing dictatorial domains that admit anonymous, unanimous, strategy-proof random social choice functions which are not random dictatorships. Our result applies to the constrained voting model. Lastly, we show that substantial strengthenings of linked domains (a class of dictatorial domains introduced in Aswal et al., 2003) are needed to restore random dictatorship and such strengthenings are “almost necessary”.     

Reclaim-proof allocation of indivisible objects

We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.     

Efficient and stable collective choices under gregarious preferences

We consider collective choice problems where a set of agents have to choose an alternative from a finite set and agents may or may not become users of the chosen alternative. An allocation is a pair given by the chosen alternative and the set of its users. Agents have gregarious preferences over allocations: given an allocation, they prefer that the set of users becomes larger. We require that the final allocation be efficient and stable (no agent can be forced to be a user and no agent who wants to be a user can be excluded). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium outcome is an efficient and stable allocation which also satisfies a maximal participation property.     

Efficient and stable collective choices under gregarious preferences

We consider collective choice problems where a set of agents have to choose an alternative from a finite set and agents may or may not become users of the chosen alternative. An allocation is a pair given by the chosen alternative and the set of its users. Agents have gregarious preferences over allocations: given an allocation, they prefer that the set of users becomes larger. We require that the final allocation be efficient and stable (no agent can be forced to be a user and no agent who wants to be a user can be excluded). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium outcome is an efficient and stable allocation which also satisfies a maximal participation property.     

On two competing mechanisms for priority-based allocation problems

We consider the priority-based allocation problem: there is a set of indivisible objects with multiple supplies (e.g., schools with seats) and a set of agents (e.g., students) with priorities over objects (e.g., proximity of residence area). We study two well-known and competing mechanisms. The agent-optimal stable mechanism (AOSM) allots objects via the deferred acceptance algorithm. The top trading cycles mechanism (TTCM) allots objects via Gale's top trading cycles algorithm. We show that the two mechanisms are equivalent, or TTCM is fair (i.e., respects agents’ priorities), or resource monotonic, or population monotonic, if and only if the priority structure is acyclic. Furthermore, if AOSM fails to be efficient (consistent) for a problem, TTCM also fails to be fair (consistent) for it. However, the converse is not necessarily true.     

Incentives in the probabilistic serial mechanism

The probabilistic serial mechanism (Bogomolnaia and Moulin, 2001 [9]) is ordinally efficient but not strategy-proof. We study incentives in the probabilistic serial mechanism for large assignment problems. We establish that for a fixed set of object types and an agent with a given expected utility function, if there are sufficiently many copies of each object type, then reporting ordinal preferences truthfully is a weakly dominant strategy for the agent (regardless of the number of other agents and their preferences). The non-manipulability and the ordinal efficiency of the probabilistic serial mechanism support its implementation instead of random serial dictatorship in large assignment problems.     

Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem

We study problems in which each of finitely many agents must be allocated a single object, based on the agents' rankings of pure outcomes. A random allocation is ordinally efficient if it is not ordinally dominated in the sense of there being another random assignment that gives each agent a first order stochastically dominant distribution of objects. We show that any ordinally efficient random assignment maximizes the sum of expected utilities for some vector of vNM utility functions that are consistent with the given ordinal preferences. One method of proof uses a new version of the separating hyperplane theorem for polyhedra. Journal of Economic Literature Classification Numbers: C78, D61.     

Mixed bundling auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.     

STRATEGY‐PROOF ALLOCATION OF INDIVISIBLE GOODS AMONG COUPLES

We consider the problem of allocating indivisible goods among couples. Agents in a couple share the indivisible good assigned to them. The main result is that an allocation rule is strategy‐proof, neutral and non‐bossy if and only if it is serially dictatorial. An allocation rule is serially dictatorial if there is a priority order of couples and a function that identifies who chooses in each couple, such that for all preference profiles, a good assigned to couple i is the best element according to the preference of the identified agent in couple i among the remaining goods when the couples with higher priorities have made their choice.     

Water allocation by social choice rules: The case of sequential rules

This paper considers the problem of allocating shares of irrigation water to different agricultural agents with single-peaked preferences with respect to their own shares. We define two different sequential allocation rules that respect the asymmetry between the agents and maintain the properties of Pareto efficiency and strategy-proofness, and we design a specific algorithm to apply these rules. The results of the empirical application of these rules for the case of an irrigated area located in the Ebro Basin (Spain) show that the designed sequential rules are able to substantially improve the efficiency of the currently applied proportional rule in context of severe scarcity of water and/or high administrative water prices.     

The optimistic stability of the core mapping in public goods production economies

Summary We show that in a production economy with public goods and a measure space of agents an allocation belongs to the core of the economy if and only if there exists no allocation in the core of a subeconomy that blocks it.We are indebted to Yossi Greenberg for very helpful suggestions, especially concerning the introduction of this work. We would also like to thank the referee for useful suggestions. Part of this work was done while the authors were visiting CORE, Université Catholique de Louvain. The support of CORE is gratefully acknowledged.     

Multiple-Object Auctions with Budget Constrained Bidders

A seller with two objects faces a group of bidders who are subject to budget constraints. The objects have common values to all bidders but need not be identical, and may be either complements or substitutes. In a simple complete information setting we show: (1) if the objects are sold by means of a sequence of open ascending auctions, then it is always optimal to sell the more valuable object first; (2) the sequential auction yields more revenue than the simultaneous ascending auction used recently by the FCC if the discrepancy in the values is large, or if there are significant complementarities; (3) a hybrid simultaneous-sequential form is revenue superior to the sequential auction; and (4) budget constraints arise endogenously.     

A Strategic Implementation of the Shapley Value for the Nested Cost‐Sharing Problem

When agents have different needs for a public facility but serving a given agent allows serving all agents with smaller needs than his without any extra cost, how should the agents divide the cost of the facility among themselves? We provide a strategic implementation of the Shapley value for this class of cost‐sharing problems. We introduce a three‐stage extensive form game that respects individual rationality and show that there is one and only one subgame‐perfect equilibrium outcome of the game. Moreover, it is the allocation assigned by the Shapley value.     

Decreasing absolute prudence: Characterization and applications to second-best risk sharing

In this paper, we provide two basic properties of utility functions u which exhibit decreasing absolute prudence i.e. (− u/u″)′ ≤ 0. These properties are used to examine the allocation of risks in an economy when some agents bear non-transferable risks. We show that it is fair Pareto-efficient to let those with a non-transferable risk bear relatively less of the transferable risk in the economy if and only if absolute prudence is decreasing. In another model, there is a complete set of contingent markets, but some agents have no direct access to them. We examine the fair efficient allocation of risk in a pool gathering a trader and a non-trader. Decreasing absolute prudence provides an upper bound to the share of the pool's risk that should be borne by the trader.     

FAIR ALLOCATION OF DISPUTED PROPERTIES

We model problems of allocating disputed properties as generalized exchange economies. Therein, agents have preferences and claims over multiple goods, and the social endowment of each good may not be sufficient to satisfy all individual claims. We focus on market‐based allocation rules that impose a two‐step procedure: assignment of rights based on claims first and voluntary exchange based on the assigned rights afterward. We characterize three focal egalitarian rights‐assignment rules that guarantee that the allocation rules are fair. We apply our results to problems of greenhouse gas emissions and contested water rights.     

Stable Assignment of Public Facilities under Congestion

We study the problem of locating multiple public facilities when each member of society has to be assigned to exactly one of these facilities. Individuals' preferences are assumed to be single‐peaked over the interval of possible locations and negatively affected by congestion. We characterize strategy‐proof, efficient, and stable allocation rules when agents have to be partitioned between two groups of users and discuss the normative content of the stability property. Finally we prove that when more than two groups have to be formed, even with common information on the distribution of the peaks, there is no strategy‐proof, efficient, and stable allocation rule.