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.

Backward Unraveling over Time: The Evolution of Strategic Behavior in the Entry-Level British Medical Labor Markets

This paper studies an adaptive artificial agent model using a genetic algorithm to analyze how a population of decision-makers learns to coordinate on the selection of an equilibrium or a social convention in a two-sided matching game. In the contexts of centralized and decentralized entry-level labor markets, evolution and adjustment paths of unraveling are explored using this model in an environment inspired by the Kagel and Roth (Quarterly Journal of Economics, 2000) experimental study. As an interesting result, it is demonstrated that stability need not be required for the success of a matching mechanism under incomplete information in the long run.Genetic algorithms, linear programming matching, stability, two-sided matching, unraveling

Internet Auctions with Artificial Adaptive Agents: A Study on Market Design

Many internet auction sites implement ascending-bid, second-price auctions. Empirically, lastminute or “late” bidding is frequently observed in “hard-close” but not in “soft-close” versions of these auctions. In this paper, we introduce an independent private-value repeated internet auction model to explain this observed difference in bidding behavior. We use finite automata to model the repeated auction strategies. We report results from simulations involving populations of artificial bidders who update their strategies via a genetic algorithm. We show that our model can deliver late or early bidding behavior, depending on the auction closing rule in accordance with the empirical evidence. As an interesting result, we observe that hard-close auctions raise less revenue than soft-close auctions. We also investigate interesting properties of the evolving strategies and arrive at some conclusions regarding both auction designs from a market design point of view.

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.

Ideology and existence of 50%-majority equilibria in multidimensional spatial voting models

When aggregating individual preferences through the majority rule in an n-dimensional spatial voting model, the `worst-case' scenario is a social choice configuration where no political equilibrium exists unless a super majority rate as high as 1-1/n is adopted. In this paper we assume that a lower d-dimensional (d smaller than n) linear map spans the possible candidates' platforms. These d `ideological' dimensions imply some linkages between the n political issues. We randomize over these linkages and show that there almost surely exists a 50%-majority equilibria in the above worst-case scenario, when n grows to infinity. Moreover the equilibrium is the mean voter. The speed of convergence (toward 50%) of the super majority rate guaranteeing existence of equilibrium is computed for d=1 and 2.

Course Bidding at Business Schools

Mechanisms that rely on course bidding are widely used at Business Schools in order to allocate seats at oversubscribed courses. Bids play two key roles under these mechanisms: Bids are used to infer student preferences and bids are used to determine who have bigger claims on course seats. We show that these two roles may easily conflict and preferences induced from bids may significantly differ from the true preferences. Therefore while these mechanisms are promoted as market mechanisms, they do not necessarily yield market outcomes. The two conflicting roles of bids is a potential source of efficiency loss part of which can be avoided simply by asking students to state their preferences in addition to bidding and thus "separating" the two roles of the bids. While there may be multiple market outcomes under this proposal, there is a market outcome which Pareto dominates any other market outcome.

Asset Price Bubbles and Crashes with Near-Zero-Intelligence Traders: Towards an Understanding of Laboratory Findings

We examine whether a simple agent--based model can generate asset price bubbles and crashes of the type observed in a series of laboratory asset market experiments beginning with the work of Smith, Suchanek and Williams (1988). We follow the methodology of Gode and Sunder (1993, 1997) and examine the outcomes that obtain when populations of zero-- intelligence (ZI) budget constrained, artificial agents are placed in the various laboratory market environments that have given rise to price bubbles. We have to put more structure on the behavior of the ZI-agents in order to address features of the laboratory asset bubble environment. We show that our model of "near--zero--intelligence" traders, operating in the same double auction environments used in several different laboratory studies, generates asset price bubbles and crashes comparable to those observed in laboratory experiments and can also match other, more subtle features of the experimental data.

A Field Experiment on Course Bidding at Business Schools

Allocation of course seats to students is a challenging task for registrars' offices in universities. Since demand exceeds supply for many courses, course allocation needs to be done equitably and efficiently. Many schools use bidding systems where student bids are used both to infer preferences over courses and to determine student priorities for courses. However, this dual role of bids can result in course allocations not being market outcomes and unnecessary efficiency loss, which can potentially be avoided with the use of an appropriate market mechanism. We report a field experiment done at the University of Michigan Business School in Spring 2004 comparing its typical course bidding mechanism with the alternate Gale-Shapley Pareto-dominant market mechanism. Our results suggest that using the latter could vastly improve efficiency of course allocation systems while facilitating market outcomes.

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.Multi-partner matching problem, Pairwise stable matching network, Credible group deviation