Selman Erol
Tepper School of Business, Carnegie Mellon University
graphons and cont. networks
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Regulating Clearing in Networks
Recent U.S. and European regulations promote centrally clearing derivatives to reduce complexity and systemic risk in the financial system. With a network model, we show that their effectiveness depends on clearing patterns. More clearing does not guarantee less systemic risk. Systemic risk can increase if multilateral netting increases at the expense of bilateral netting. We study confidential derivatives regulatory data and find evidence that contagion is less likely to start in the core but more likely to spread from the core. We introduce concepts of complexity and centrality within the financial network, exploring their implications for stability and regulatory oversight.
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.
Insider Networks
How do insiders respond to regulatory oversight on the use of insider information? History suggests that they form more sophisticated networks to circumvent regulation. We develop a theory of the formation and regulation of insider information networks. We show that agents with sufficiently complex networks bypass any given regulatory environment. In response, regulators employ broad regulatory boundaries to combat gaming. Tighter regulation induces agents to migrate activity from existing social networks to a core-periphery insider network. A small group of agents endogenously arise as intermediaries for the bulk of transmissions.
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.
While networks offer substantial benefits, they also facilitate the spread of major public threats such as misinformation in social networks, supply chain disruptions, cascading failures of interconnected banks, and epidemics. Efforts by authorities to mitigate contagion can inadvertently diminish agents’ incentives to guard against it. This effect is amplified by the network itself, which can counteract the intended benefits of these mitigating measures. Specifically, as more effective tools are deployed to combat contagion, the interplay between mitigation efforts and endogenous network formation create a “network hazard,” leading to reduced welfare, increased contagion, and greater volatility.
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.
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.