Stochastic stability for roommate markets

We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have been proposed to extend the core to all roommate markets (including those with an empty core). An important implication of our results is that the set of absorbing matchings is the only solution concept that is core consistent and shares the stochastic stability characteristic with the core.     

Matching through position auctions

Using a mechanism design framework, we characterize how a profit-maximizing intermediary can design matching markets when each agent is privately informed about his quality as a partner. Sufficient conditions are provided that ensure a version of positive assortative matching (what we call truncated positive assortative matching) maximizes profits. Under these conditions, all-pay position auctions always implement the profit-maximizing allocation. Winners-pay position auctions, however, only do so in sufficiently large markets.     

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.     

Ordinal efficiency and dominated sets of assignments

Using lotteries is a common tool for allocating indivisible goods. Since obtaining preferences over lotteries is often difficult, real-life mechanisms usually rely on ordinal preferences over deterministic outcomes. Bogomolnaia and Moulin (J. Econom. Theory 19 (2002) 623) show that the outcome of an ex post efficient mechanism may be stochastically dominated. They define a random assignment to be ordinally efficient if and only if it is not stochastically dominated. In this paper we investigate the relation between ex post efficiency and ordinal efficiency. We introduce a new notion of domination defined over sets of assignments and show that a lottery induces an ordinally efficient random assignment if and only if each subset of the full support of the lottery is undominated.     

The roommates problem revisited

One of the oldest matching problems is Gale and Shapley's (1962) [8] “roommates problem”: is there a stable way to assign 2N students into N roommate pairs? Unlike the classic marriage problem or college admissions problem, there need not exist a stable solution to the roommates problem. However, stability ignores the key physical constraint that roommates require a room and is therefore too restrictive. This motivates a new matching problem: matching agents subject to an initial assignment. A particularly important example is kidney exchange where after an assignment has been made, subsequent tests may determine that a patient and donor are incompatible. This paper introduces an efficient algorithm for finding a Pareto improvement starting from any status quo roommates assignment.     

Kidney exchange: An egalitarian mechanism

Kidney exchange programs utilize both deceased-donor and live-donor kidneys. One of these programs, a two-way kidney paired donation (KPD), involves two patients exchanging their live donors? kidneys. Another possibility is a list exchange (LE): a living incompatible donor provides a kidney to a candidate on the deceased-donor waitlist and in return the intended recipient of this donor receives a priority on the waitlist. By taking into consideration the fact that transplants from live donors have a higher chance of success than those from cadavers, we characterize the set of efficient and egalitarian exchanges involving the KPD?s and LE?s.     

Monotonic and implementable solutions in generalized matching problems

We consider one-to-one matching problems when preferences are weak orders and search for (Maskin-)monotonic and implementable solutions. We show that for any coalition structure , the strong -core is monotonic if and only if it is the individually rational solution. We introduce a solution, which we call the “union strong -core”, and show that this solution is the minimal way to expand the strong -core recovering monotonicity. We also show that the union strong -core is implementable.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

The computational complexity of random serial dictatorship

In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is a well-known generalization of random dictatorship that retains both properties. RSD has been particularly successful in the special domain of random assignment where indifferences are unavoidable. While executing RSD is obviously feasible, we show that computing the resulting probabilities is #P-complete, and thus intractable, both in the context of voting and assignment.     

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.     

Coase theorem, complexity and transaction costs

This paper, by introducing complexity considerations, provides a dynamic foundation for the Coase theorem and highlights the role of transaction costs in generating inefficient bargaining/negotiation outcomes. We show, when the players have a preference for less complex strategies, the Coase theorem holds in negotiation models with repeated surplus and endogenous disagreement payoffs if and only if there are no transaction costs. Specifically, complexity considerations select only efficient equilibria in these models without transaction costs while every equilibrium induces perpetual disagreement and inefficiency with transaction costs. We also show the latter is true in the Rubinstein bargaining model with transaction costs.     

Indeterminacy and directed search

The directed search approach assumes each seller posts a fixed price and, ex post, randomly allocates the good should more than one buyer desire the good. This paper assumes sellers can post prices which are contingent on ex post realized demand; e.g. an advertisement might state the Bertrand price should there be more than one buyer, which corresponds to an auction outcome. Competition in fixed prices and ex post rationing describes equilibrium behavior. There is also real market indeterminacy: a continuum of equilibria exists which are not payoff equivalent. Sellers prefer the equilibrium in auctions.     

Representing roommates’ preferences with symmetric utilities

In the context of the stable roommates problem, it is shown that acyclicity of preferences is equivalent to the existence of symmetric utility functions, i.e. the utility of agent i when matched with j is the same as j's utility when matched with i.     

Classifying exchange rate regimes: Deeds vs. words

Most of the empirical literature on exchange rate regimes uses the IMF de jure classification based on the regime announced by the governments, despite the recognized inconsistencies between reported and actual policies in many cases. To address this problem, we construct a de facto classification based on data on exchange rates and international reserves from all IMF-reporting countries over the period 1974-2000, which we believe provides a meaningful alternative for future empirical work on the topic. The classification sheds new light on several stylized facts previously reported in the literature. In particular, we find that the de facto pegs have remained stable throughout the last decade, although an increasing number of them shy away from an explicit commitment to a fixed regime (“hidden pegs”). We confirm the hollowing out hypothesis but show that it does not apply to countries with limited access to capital markets. We also find that pure floats are associated with only relatively minor nominal exchange rate volatility and that the recent increase in the number of de jure floats goes hand in hand with an increase in the number of de facto dirty floats (“fear of floating”).     

Disappearing private reputations in long-run relationships

For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps et al. [Imperfect monitoring and impermanent reputations, Econometrica 72 (2004) 407-432] showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is private. The rate at which reputations disappear is uniform across equilibria and reputations also disappear in sufficiently long discounted finitely repeated games.     

Delays and partial agreements in multi-issue bargaining

We model a situation in which two players bargain over two pies, one of which can only be consumed starting at a future date. Suppose the players value the pies asymmetrically: one player values the existing pie more than the future one, while the other player has the opposite valuation. We show that players may consume only a fraction of the existing pie in the first period, and then consume the remainder of it, along with the second pie, at the date at which the second pie becomes available. Thus, our model features a special form of bargaining delay, in which agreements take place in multiple stages. Such partial agreements arise when players are patient enough, when they expect the second pie to become available soon, and when the asymmetry in their valuations is large enough.     

A simple sufficient condition for strong implementation

In an important step forward Maskin [E. Maskin, Nash equilibrium and welfare optimality, Rev. Econ. Stud. 66 (1999) 23–38] showed that two properties – monotonicity and no veto power – are together sufficient for Nash implementation. In contrast to the vast literature that followed, this characterization has two major advantages: First, it is often easy to verify, and second, it has an elegant and simple interpretation. However, there does not exist a similar condition for social choice correspondences that are implementable in strong equilibrium. All existing characterizations are either hard to verify or apply only to comprehensive preference domains. In this paper we improve the situation by giving one such condition. Moreover, using well-known examples we show that this is a practical tool.     

Von Neumann-Morgenstern stable sets in matching problems

The following properties of the core of a one-to-one matching problem are well-known: (i) the core is non-empty; (ii) the core is a distributive lattice; and (iii) the set of unmatched agents is the same for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (Von Neumann-Morgenstern) stable sets in one-to-one matching problems. We show that a set V of matchings is a stable set of a one-to-one matching problem only if V is a maximal set satisfying the following properties: (a) the core is a subset of V; (b) V is a distributive lattice; and (c) the set of unmatched agents is the same for all matchings belonging to V. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b), and (c).     

Proportional concessions and the leximin solution

In this note we introduce a new axiom for bargaining solutions, named Proportional Concession Monotonicity (PCM), which imposes that no player benefits when all players collectively make proportional concessions with respect to their respective utopia values. We reconsider the leximin solution (Imai, 1983), and obtain an alternative characterization on the basis of PCM.     

Does resorting to online dispute resolution promote agreements? Experimental evidence

This paper presents an experiment performed to test the properties of an innovative bargaining mechanism (called automated negotiation) used to resolve disputes arising from Internet-based transactions. The main result shows that the settlement rule tends to chill bargaining as it creates incentives for individuals to misrepresent their true valuations, which implies that automated negotiation is not able to promote agreements. However, this perverse effect depends strongly on the conflict situation. When the threat that a disagreement occurs is more credible, the strategic effect is reduced since defendants are more interested in maximizing the efficiency of a settlement than their own expected profit. The implications of these results are then used to discuss the potential role of public regulation and reputation mechanisms in Cyberspace.