Elizabeth Bodine-Baron

Peer effects and stability in matching markets

Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In all these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings. In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social network. The key feature of our model is that it captures peer effects and complementarities using utility functions, rather than traditional preference ordering. With this model and considering a weaker notion of stability, namely twosided exchange stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. To characterize the efficiency of matching markets with externalities, we provide general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

Minimizing the Social Cost of an Epidemic

In this paper we quantify the total cost of an epidemic spreading through a social network, accounting for both the immunization and disease costs. Previous research has typically focused on determining the optimal strategy to limit the lifetime of a disease, without considering the cost of such strategies. In the large graph limit, we calculate the exact expected disease cost for a general random graph, and we illustrate it for the specific example of an Erdos-Renyi network. We also give an upper bound on the expected disease cost for finite-size graphs, and show through simulation that the upper bound is tight for Erdos-Renyi networks and graphs with exponential degree distributions. Finally, we study how to optimally perform a one-shot immunization to minimize the social cost of a disease, including both the cost of the disease and the cost of immunization.

Distance-Dependent Kronecker Graphs for Modeling Social Networks

This paper focuses on a generalization of stochastic Kronecker graphs, introducing a Kronecker-like operator and defining a family of generator matrices H dependent on distances between nodes in a specified graph embedding. We prove that any lattice-based network model with sufficiently small distance-dependent connection probability will have a Poisson degree distribution and provide a general framework to prove searchability for such a network. Using this framework, we focus on a specific example of an expanding hypercube and discuss the similarities and differences of such a model with recently proposed network models based on a hidden metric space. We also prove that a greedy forwarding algorithm can find very short paths of length O((log log n)2) on the hypercube with n nodes, demonstrating that distance-dependent Kronecker graphs can generate searchable network models.

A symmetric adaptive algorithm for speeding-up consensus

Performing distributed consensus in a network has been an important research problem for several years, and is directly applicable to sensor networks, autonomous vehicle formation, etc. While there exists a wide variety of algorithms that can be proven to asymptotically reach consensus, in applications involving time-varying parameters and tracking, it is often crucial to reach consensus “as quickly as possible”. In [?] it has been shown that, with global knowledge of the network topology, it is possible to optimize the convergence time in distributed averaging algorithms via solving a semi-definite program (SDP) to obtain the optimal averaging weights. Unfortunately, in most applications, nodes do not have knowledge of the full network topology and cannot implement the required SDP in a distributed fashion. In this paper, we present a symmetric adaptive weight algorithm for distributed consensus averaging on bi-directional noiseless networks. The algorithm uses an LMS (Least Mean Squares) approach to adaptively update the edge weights used to calculate each nodes values. The derivation shows that global error can be minimized in a distributed fashion and that the resulting adaptive weights are symmetric—symmetry being critical for convergence to the true average. Simulations show that convergence time is nearly equal to that of a non-symmetric adaptive algorithm developed in [?], and significantly better than that of the non-adaptive Metropolis-Hastings algorithm. Most importantly, our symmetric adaptive algorithm converges to the sample mean, whereas the method of [?] converges to an arbitrary value and results in significant error.

What is the global landpower network and what value might it provide

ABSTRACT US national security guidance, as well as the US Army’s operational experiences since 2001, emphasizes the importance of working closely with partner countries to achieve US strategic objectives. The US Army has introduced the global landpower network (GLN) concept as a means to integrate, sustain and advance the Army’s considerable ongoing efforts to meet US national security guidance. This study develops the GLN concept further, and addresses three questions. What benefits can the GLN provide the Army? What are the essential components of the GLN? What options exist for implementing the GLN concept? By developing the GLN concept, the Army has the opportunity to transition the GLN from an often ad hoc and reactive set of relationships to one that the Army more self-consciously prioritizes and leverages as a resource to meet US strategic objectives.