Selman Erol
Tepper School of Business, Carnegie Mellon University
graphons and continuous networks
Paper Types:
Regulating Clearing in Networks
Recent regulations in the U.S. and Europe incentivize the use of central counterparty clearing houses (CCP) to clear derivatives, arguably to create a less complex and more transparent interbank network that is less prone to financial instabilities. We construct a network model with endogenous exposures and show that the core and the periphery react asymmetrically to these regulations. The core values opacity more and adopts clearing less. Consequently, bilaterally netted exposures to the core increase. The regulation also makes the CCP more exposed to the core than the periphery was pre-regulation. This endogenous network reaction to the regulation creates the unanticipated effect of reducing financial stability through more frequent coordination failures that start at the core and spread to the periphery and the CCP. A novel dataset on U.S. counterparty exposures, before and after the regulations, confirm the model’s testable implications.
Insider Networks
How do insiders respond to regulatory oversight? History suggests that they form sophisticated networks to share information and circumvent regulation. We develop a theory of the formation and regulation of information transmission networks. We show that agents with sufficiently complex networks bypass any given regulatory environment. In response, regulators employ broad regulatory boundaries to combat gaming, giving rise to regulatory ambiguity. Tighter regulation induces agents to migrate transmission activity from existing social networks to a core-periphery insider network. A small group of agents endogenously arise as intermediaries for the bulk of information. We provide centrality measures that identify intermediaries.
Civil Liberties and Social Structure
Governments use coercion to aggregate distributed information relevant to governmental objectives –from the prosecution of regime-stability threats to terrorism or epidemics–. A cohesive social structure facilitates this task, as reliable information will often come from friends and acquaintances. A cohesive citizenry can more easily exercise collective action to resist such coercion, however. We present an equilibrium theory where this tension mediates the joint determination of social structure and civil liberties. We show that segregation and unequal treatment sustain each other as coordination failures: citizens choose to segregate along the lines of an arbitrary trait only when the government exercises unequal treatment as a function of the trait, and the government engages in unequal treatment only when citizens choose to segregate based on the trait. We characterize when unequal treatment against a minority or a majority can be sustained, and how equilibrium social cohesiveness and civil liberties respond to the arrival of widespread surveillance technologies, shocks to collective perceptions about the likelihood of threats or the importance of privacy, or to community norms such as codes of silence.
Network Hazard and Superspreaders
Higher availability and efficacy of protective measures against infectious diseases, such as vaccines, increases individuals’ propensity to socialize. Consequently, the number of visits to central points of interest (e.g., schools, gyms, grocery stores) and the rate of interactions with the agents employed therein (e.g., teachers, trainers, cashiers) increase. This opens more channels for the virus to transmit through the central agent or location. This leads to a manifestation of network hazard (Erol 2019). The infection rates can increase as protective measures become more effective and more available. Testable predictions of the theory are confirmed by the foot traffic data from 2019-2022 and historical COVID-19 vaccination and community transmission rates.
Contagion in Graphons
The analysis of threshold contagion processes in large networks is challenging. While the lack of accurate network data is often a major obstacle, finding optimal interventions is computationally intractable even in well-measured large networks. To obviate these issues we consider threshold contagion over networks sampled from a graphon—a flexible stochastic network formation model—and show that in this case the contagion outcome can be predicted by only exploiting information about the graphon. To this end, we exploit a second interpretation of graphons as graph limits to formally define a threshold contagion process on a graphon for infinite populations. We then show that contagion in large but finite sampled networks is well approximated by graphon contagion. This convergence result suggests that one can design interventions for large sampled networks by first solving the equivalent problem for an infinite population interacting according to the limiting graphon. We show that, under suitable regularity assumptions, the latter is a tractable problem and we provide analytical characterizations for the extent of contagion and for optimal seeding policies in graphons with both finite and infinite agent types.
Social and Economic Distancing
Dealing with pandemics, such as the recent COVID-19 virus, has highlighted the critical role of social distancing to avoid contagion and deaths. New technologies that allow replacing in-person for at-distance activities have blurred the mapping between social and economic distancing. In this paper we model how individuals react to social distancing guidelines by changing their network of economic relations, affecting total output, wealth inequality, and long-term growth.