Migration as Submodular Optimization

Migration presents sweeping societal challenges that have recently attracted significant attention from the scientific community. One of the prominent approaches that have been suggested employs optimization and machine learning to match migrants to localities in a way that maximizes the expected number of migrants who find employment. However, it relies on a strong additivity assumption that, we argue, does not hold in practice, due to competition effects; we propose to enhance the data-driven approach by explicitly optimizing for these effects. Specifically, we cast our problem as the maximization of an approximately submodular function subject to matroid constraints, and prove that the worst-case guarantees given by the classic greedy algorithm extend to this setting. We then present three different models for competition effects, and show that they all give rise to submodular objectives. Finally, we demonstrate via simulations that our approach leads to significant gains across the board.Comment: Simulation code is available at https://github.com/pgoelz/migration

Matching games with partial information

We analyze different ways of pairing agents in a bipartite matching problem, with regard to its scaling properties and to the distribution of individual ``satisfactions''. Then we explore the role of partial information and bounded rationality in a generalized {\it Marriage Problem}, comparing the benefits obtained by self-searching and by a matchmaker. Finally we propose a modified matching game intended to mimic the way consumers' information makes firms to enhance the quality of their products in a competitive market.Comment: 19 pages, 8 fig

Economic Efficiency Requires Interaction

We study the necessity of interaction between individuals for obtaining approximately efficient allocations. The role of interaction in markets has received significant attention in economic thinking, e.g. in Hayek's 1945 classic paper. We consider this problem in the framework of simultaneous communication complexity. We analyze the amount of simultaneous communication required for achieving an approximately efficient allocation. In particular, we consider two settings: combinatorial auctions with unit demand bidders (bipartite matching) and combinatorial auctions with subadditive bidders. For both settings we first show that non-interactive systems have enormous communication costs relative to interactive ones. On the other hand, we show that limited interaction enables us to find approximately efficient allocations

Mechanism design for dynamic double auctions

Cette thèse a pour objet de concevoir des mécanismes d'allocation dans le contexte des enchères doubles dynamiques (achats groupés, bourses électroniques). Le principal défi inhérent à la conception de tels mécanismes est d'aboutir à un résultat socialement optimal alors que la dynamique induit une incertitude sur les arrivées et départs des participants de l'enchère ainsi que sur les valuations qui peuvent être fluctuantes. Dans cette thèse, nous proposons des mécanismes qui sont efficaces, incitatifs et garantissant l'équilibre du budget. La définition de ces mécanismes s'appuient sur les algorithmes d'appareillage pour des graphes bipartis (technique d'augmentation et réduction) ainsi que sur une méthode générale prenant en compte le comportement des participants.This thesis addresses the problem of designing mechanisms that lead to socially desirable outcomes in dynamic double auction markets such as stock exchanges and group buying. The main challenge of the design is dealing with the uncertainty posed by the participants who are dynamically arriving and departing and their valuations vary over time. The thesis demonstrates the difficulties in designing mechanisms with desirable properties such as truthfulness, efficiency and budget balance. It also provides dedicated mechanisms satisfying those properties by using augmentation, reduction and behaviour-based approaches

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

Skills diversity in unity

At any point in time, skills gaps, mismatches, and shortages arise because of an imperfect correspondence between the singular sets of skills required by different open vacancies and the unique combinations of capabilities embodied in every job seeker - skills diversity in unity. This paper first constructs an abstract framework for defining and thinking about these phenomena in a unified, formal and objective way. The main building block is a discrete skills space in which the locations of vacancies and workers are determined by the vectors of skills characterizing them. We define skills gaps and mismatches as two different distance measures between them, and derive a condition for each vacancy that determines whether or not it experiences a skills shortage. We then develop a job matching model with imperfect information, in which skills mismatches influence the job application decisions of the workers, while skills gaps and shortages shape the competition for workers on the resulting bipartite job applications network. The tools proposed in this paper could in future work be employed as the main ingredients of an agent-based model used to investigate how skills gaps, mismatches and shortages affect equilibrium outcomes in the context of skills diversity in unity and imperfect informatio