On the Survival of Some Unstable Two-Sided Matching Mechanisms

In the 1960s, three types of matching mechanisms were adopted in regional entry-level British medical labor markets to prevent unraveling of contract dates. One of these categories of matching mechanisms failed to prevent unraveling. Roth (1991) showed the instability of that failing category. One of the surviving categories was unstable as well, and Roth concluded that features of the environments of these mechanisms are responsible for their survival. However, Ünver (2001) demonstrated that the successful yet unstable mechanisms performed better in preventing unraveling than the unsuccessful and unstable category in an artificial-adaptive-agent-based economy. In this paper, we conduct a human subject experiment in addition to short- and long-run artificial agent simulations to understand this puzzle. We find that both the unsuccessful and unstable mechanism and the successful and unstable mechanism perform poorly in preventing unraveling in the experiment and in short-run simulations, while long-run simulations support the previous Ünver finding.

Credible Group Stability in Multi-Partner Matching Problems

It is known that in two-sided many-to-many matching markets, pair-wise stability is not logically related with the (weak) core, unlike in many-to-one matching markets (Blair, 1988). In this paper, we seek a theoretical foundation for pairwise stability when group deviations are allowed. Group deviations are defined in graphs on the set of agents. We introduce executable group deviations in order to discuss the credibility of group deviations and to defined credibly group stable matchings. We show, under responsive preferences, that credible group stability is equivalent to pairwise stability in the multi-partner matching problem that includes two-sided matching problems as special cases. Under the same preference restriction, we also show the equivalence between the set of pairwise stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic form game. However, under a weaker preference restriction, substitutability, these equivalences no longer hold, since pairwise stable matchings may be strictly Pareto-ordered, unlike under responsiveness.Multi-partner matching problem, Pairwise stable matching network, Credible group deviation

Credible Group Stability in Many-to-Many Matching Problems

It is known that in two-sided many-to-many matching problems, pairwise stable matchings may not be immune to group deviations, unlike in many- to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise- responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.

House Allocation with Existing Tenants: An Equivalence

In this paper we analyze two house allocation mechanisms each of which is designed to eliminate inefficiencies in real-life house allocation problems where there are both existing tenants and newcomers. The first mechanism chooses the unique core allocation of a "sister" exchange economy which is constructed by assigning each existing tenant her current house and randomly assigning each newcomer a vacant house. The second mechanism -top trading cycles mechanism- first chooses an ordering from a given distribution and next determines the final outcome as follows: Assign first agent her top choice, next agent her top choice among remaining houses and so on, until someone demands house of an existing tenant who is still in the line. At that point modify the queue by inserting her at the top and proceed. Similarly, insert any existing tenant who is not already served at the top of the queue once her house is demanded. Whenever a loop of existing tenants forms, assign each of them the house she demands and proceed. Our main result is that the core based mechanism is equivalent to an extreme case of the top trading cycles mechanism which orders newcomers before the existing tenants.

Credible Group Stability in Multi-Partner Matching Problems

It is known that in two-sided many-to-many matching markets, pair-wise stability is not logically related with the (weak) core, unlike in many-to-one matching markets (Blair, 1988). In this paper, we seek a theoretical foundation for pairwise stability when group deviations are allowed. Group deviations are defined in graphs on the set of agents. We introduce executable group deviations in order to discuss the credibility of group deviations and to defined credibly group stable matchings. We show, under responsive preferences, that credible group stability is equivalent to pairwise stability in the multi-partner matching problem that includes two-sided matching problems as special cases. Under the same preference restriction, we also show the equivalence between the set of pairwise stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic form game. However, under a weaker preference restriction, substitutability, these equivalences no longer hold, since pairwise stable matchings may be strictly Pareto-ordered, unlike under responsiveness

Outside options in neutral allocation of discrete resources

Serial dictatorships have emerged as the canonical simple mechanisms in the literature on the allocation of indivisible goods without transfers. They are the only neutral and group-strategy-proof mechanisms in environments in which agents have no outside options and hence no individual rationality constraints (Svensson in Soc Choice Welfare 16:557–567, 1999). Accounting for outside options and individual rationality constraints, our main result constructs the class of group-strategy-proof, neutral, and non-wasteful mechanisms. These mechanisms are also Pareto efficient and we call them binary serial dictatorships. The abundance of the outside option - anybody who wants can opt out to get it - is crucial for our result

Pairwise Kidney Exchange

The theoretical literature on exchange of indivisible goods finds natural application in organizing the exchange of live donor kidneys for transplant. However, in kidney exchange, there are constraints on the size of feasible exchanges. Initially, kidney exchanges are likely to be pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than larger exchanges. Furthermore, the experience of many American surgeons suggests to them that preferences over kidneys are approximately 0-1, i.e. that patients and surgeons should be largely indifferent among healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival probabilities, regardless of the closeness of tissue types between patient and donor. We show that, although the pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences. This class of mechanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use to allocate cadaver organs, as well as stochastic mechanisms that allow distributive justice issues to be

Two-sided matching via balanced exchange: Tuition and worker exchanges

We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchange, in which each firm has to avoid being a net-exporter of workers. These exchanges use decentralized markets, making it difficult to achieve a balance between exports and imports. We show that stable equilibria discourage net-exporting firms from exchange. We introduce the two-sided top-trading-cycles mechanism that is balanced-efficient, worker-strategy-proof, acceptable, and individually rational, and respects priority bylaws regarding worker eligibility. We prove that it is the unique mechanism fulfilling these objectives. Moreover, it encourages exchange, since full participation is the dominant strategy for firms

A Kidney Exchange Clearinghouse in New England

Economic