Stochastic Stability for Roommate Markets

We show that for any roommate market the set of stochastically stable matchings coincideswith 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 beenproposed 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 onlysolution concept that is core consistent and shares the stochastic stability characteristic withthe core.Economics (Jel: A)

Matching Dynamics with Constraints

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times. For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of "consistent" instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated. We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.Comment: Conference Version in WINE 201

Usability Test of Personality Type within a Roommate Matching Website: A Case Study

We designed and built a roommate matching website, exclusively for students, which allow students to have a central point in which they can meet credible roommate candidates, search for verified housing, and easily reach out to these individuals to further their relationship, and eventually share living space. Our website aims to allow a user to search for compatible roommates not just by living habits, but by tying in the personality of candidates in reference to their own personality type. This type of personality matching in conjunction with a standard behavioral survey is the basis of the algorithm used for roommate matching. In addition to designing and building this website, we also conducted a research around two questions. First, does the idea of personality type in conjunction with living habits have the capacity to form a stronger foundation on which roommates can be selected? Second, is there a means in which we can collect this information from a user and apply it, while avoiding the typical result of survey fatigue that is inherent in existing personality quizzes? We found that majority of our respondents felt that knowing the personality compatibility would influence their decision of sharing a living space with someone. Our respondents also preferred a more visual and interactive quiz to determine personality type in comparison to questionnaires

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

Locally Stable Marriage with Strict Preferences

We study stable matching problems with locality of information and control. In our model, each agent is a node in a fixed network and strives to be matched to another agent. An agent has a complete preference list over all other agents it can be matched with. Agents can match arbitrarily, and they learn about possible partners dynamically based on their current neighborhood. We consider convergence of dynamics to locally stable matchings -- states that are stable with respect to their imposed information structure in the network. In the two-sided case of stable marriage in which existence is guaranteed, we show that the existence of a path to stability becomes NP-hard to decide. This holds even when the network exists only among one partition of agents. In contrast, if one partition has no network and agents remember a previous match every round, a path to stability is guaranteed and random dynamics converge with probability 1. We characterize this positive result in various ways. For instance, it holds for random memory and for cache memory with the most recent partner, but not for cache memory with the best partner. Also, it is crucial which partition of the agents has memory. Finally, we present results for centralized computation of locally stable matchings, i.e., computing maximum locally stable matchings in the two-sided case and deciding existence in the roommates case.Comment: Conference version in ICALP 2013; to appear in SIAM J. Disc Mat

Paths to stability in two-sided matching under uncertainty

We consider one-to-one matching problems under two modalities of uncertainty in which types are assigned to agents either with or without replacement. Individuals have preferences over the possible types of the agents from the opposite market side and initially know the ‘name’ but not the ‘type’ of their potential partners. In this context, learning occurs via matching and using Bayes’ rule. We introduce the notion of a stable and consistent outcome, and show how the interaction between blocking and learning behavior shapes the existence of paths to stability in each of these two uncertainty environments. Existence of stable and consistent outcomes then follows as a side result

Decentralized matching markets : a laboratory experiment

We report data from controlled laboratory experiments on two-sided matching markets in which participants interact in a decentralized way, without having to refer to a central clearinghouse. Our treatments have been designed to evaluate the effect of information, search costs, and binding agreements on the final outcome and also on the individual strategies that lead to it. We find that these features affect the level and pace of market activity as well as the identity of those who receive proposals. While the lack of information alone does not reduce stability or efficiency, its combination with search costs can be detrimental.Financial support from Fundação para a Ciência e Tecnologia (FCCN); Juan de la Cierva program of the Spanish Ministry of Science and Innovation

A one-shot deviation principle for stability in matching problems

This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation