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Research Mentor and Department
Professor Jane Butterfield
By looking at network formation and risk associated with creating relationships, Blume et. al. (2011) were able to model cascading failure over multi-step paths using graph theory. Applications of such failure include financial contagion, modeling epidemic disease, and the exposure of covert organizations to discovery, among others. In graph theory terms, the goal in all of these applications is to form graphs in which cascading failure is unlikely. Blume et. al. were able to prove that the formation of disjoint cliques, or subsets of a graph in which all vertices (participants) in each subset do not form edges (relationships) with vertices not in the subset, has this property.
This poster focuses on how Blume’s model of financial contagion, the transmission of financial shock from one participant to another, can be applied to recent macroeconomic events. The Financial Crisis of 2008 was an event that demonstrated the consequences of contagious risk in networks. It is commonly accepted that higher risk yields higher reward. Higher risk taken by banks in 2008 posed a threat not only to the two primary participants in the agreement, but also all participants in the network of agreements that could be reached via multi-step paths. In addition, we show how social optimality affects payoffs and the stability of economies by analyzing banking systems in countries with centralized and decentralized governments. Lastly, we explore an application related to market structure. Electronic, digital currencies, such as Bitcoin and Canada’s Mintchip, are commonly used as a form of investment. However, these investments solely rely on the willingness of users to accept this form of currency. It has been shown that a large portion of Bitcoin investments default due to the anonymous nature of the transactions.
Research was supervised by Professor Jane Butterfield, University of Minnesota--Twin Cities, and supported by the Math Center for Educational Programs, Department of Mathematics, University of Minnesota.