Experimental results on the roommate problem

We use laboratory experiments to analyze decentralized decision-making in one-sided matching markets. We find that subjects tend to make decisions in line with theoretical models, as their offering and accepting decisions are only guided by the objective of improving upon the status quo. However, isolated individual mistakes, that do not disappear with experience or time, often make theoretically-stable matchings unstable in the laboratory. Markets with incomplete infor- mation are especially prone to this problem.convergence, experiments, one-sided matching, stability

A Measure to Compare Matchings in Marriage Markets

In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly “disruptive” subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: the subset is a justified objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison.Stable Marriage Problem, Matching, Blocking Pair, Instability, Matching Comparison, Decentralized Market, Bargaining Set

Preference Structure and Random Paths to Stability in Matching Markets

This paper examines how preference correlation and intercorrelation combine to influence the length of a decentralized matching market's path to stability. In simulated experiments, marriage markets with various preference specifications begin at an arbitrary matching of couples and proceed toward stability via the random mechanism proposed by Roth and Vande Vate (1990). The results of these experiments reveal that fundamental preference characteristics are critical in predicting how long the market will take to reach a stable matching. In particular, intercorrelation and correlation are shown to have an exponential impact on the number of blocking pairs that must be randomly satisfied before stability is attained. The magnitude of the impact is dramatically different, however, depending on whether preferences are positively or negatively intercorrelated.

Multi-agent Learning For Game-theoretical Problems

Multi-agent systems are prevalent in the real world in various domains. In many multi-agent systems, interaction among agents is inevitable, and cooperation in some form is needed among agents to deal with the task at hand. We model the type of multi-agent systems where autonomous agents inhabit an environment with no global control or global knowledge, decentralized in the true sense. In particular, we consider game-theoretical problems such as the hedonic coalition formation games, matching problems, and Cournot games. We propose novel decentralized learning and multi-agent reinforcement learning approaches to train agents in learning behaviors and adapting to the environments. We use game-theoretic evaluation criteria such as optimality, stability, and resulting equilibria

Clearinghouses for two-sided matching: An experimental study

We experimentally study the Gale and Shapley, 1962 mechanism, which is utilized in a wide set of applications, most prominently the National Resident Matching Program (NRMP). Several insights come out of our analysis. First, only 48% of our observed outcomes are stable, and among those a large majority culminate at the receiver-optimal stable matching. Second, receivers rarely truncate their true preferences: it is the proposers who do not make offers in order of their preference, frequently skipping potential partners. Third, market characteristics affect behavior: both the cardinal representation and core size influence whether laboratory outcomes are stable. We conclude by using our controlled results and a behavioral model to shed light on a number of stylized facts we derive from new NRMP survey and outcome data, and to explain the small cores previously documented for the NRMP

"Almost-stable" matchings in the Hospitals / Residents problem with Couples

The Hospitals / Residents problem with Couples (hrc) models the allocation of intending junior doctors to hospitals where couples are allowed to submit joint preference lists over pairs of (typically geographically close) hospitals. It is known that a stable matching need not exist, so we consider min bp hrc, the problem of finding a matching that admits the minimum number of blocking pairs (i.e., is “as stable as possible”). We show that this problem is NP-hard and difficult to approximate even in the highly restricted case that each couple finds only one hospital pair acceptable. However if we further assume that the preference list of each single resident and hospital is of length at most 2, we give a polynomial-time algorithm for this case. We then present the first Integer Programming (IP) and Constraint Programming (CP) models for min bp hrc. Finally, we discuss an empirical evaluation of these models applied to randomly-generated instances of min bp hrc. We find that on average, the CP model is about 1.15 times faster than the IP model, and when presolving is applied to the CP model, it is on average 8.14 times faster. We further observe that the number of blocking pairs admitted by a solution is very small, i.e., usually at most 1, and never more than 2, for the (28,000) instances considered

Fast distributed almost stable marriages

In their seminal work on the Stable Marriage Problem, Gale and Shapley describe an algorithm which finds a stable matching in $O(n^2)$ communication rounds. Their algorithm has a natural interpretation as a distributed algorithm where each player is represented by a single processor. In this distributed model, Floreen, Kaski, Polishchuk, and Suomela recently showed that for bounded preference lists, terminating the Gale-Shapley algorithm after a constant number of rounds results in an almost stable matching. In this paper, we describe a new deterministic distributed algorithm which finds an almost stable matching in $O(\log^5 n)$ communication rounds for arbitrary preferences. We also present a faster randomized variant which requires $O(\log^2 n)$ rounds. This run-time can be improved to $O(1)$ rounds for "almost regular" (and in particular complete) preferences. To our knowledge, these are the first sub-polynomial round distributed algorithms for any variant of the stable marriage problem with unbounded preferences.Comment: Various improvements in version 2: algorithms for general (not just "almost regular") preferences; deterministic variant of the algorithm; streamlined proof of approximation guarante

A measure to compare matchings in marriage markets

In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly disruptive subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: The subset is a justifed objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison