Adam Smith Business School

Professor Simone Cerreia-Vioglio, Bocconi University

"Nonlinear Fixed Points and Stationarity: Economic Applications"
Tuesday, 14 November 2023. 4 pm
Room 355 Gilbert Scott Building

Abstract

We consider the fixed points of nonlinear operators that naturally arise in games and general equilibrium models with endogenous networks, dynamic stochastic games, in models of opinion dynamics with stubborn agents, and financial networks. We study limit cases that correspond to high coordination motives, infinite patience, vanishing stubbornness in the applications above, and small exposure to the real sector. Under monotonicity and continuity assumptions, we provide explicit expressions for the limit fixed points. We show that, under differentiability, the limit fixed point is linear in the initial conditions and characterized by the Jacobian of the operator at any constant vector with an explicit and linear rate of convergence. Without differentiability, but under additional concavity properties, the multiplicity of Jacobians is resolved by a representation of the limit fixed point as a maxmin functional evaluated at the initial conditions. In our applications, we use these results to characterize the limit equilibrium actions, prices, and endogenous networks, show the existence of the asymptotic value in a class of zero-sum stochastic games with a continuum of actions, compute a nonlinear version of the eigenvector centrality of agents
in networks, and the characterize the equilibrium loss evaluations in financial networks.

Bio

I earned my Laurea degree in Economics from Bocconi University in 2005 and my PhD in Economics from Columbia University in 2010. I joined Bocconi in 2010 as an Assistant Professor. I work in Economic Theory and Applied Mathematics.
I won an Advanced ERC research grant from the European Research Council (2016-2021).

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For further information, please contact business-school-research@glasgow.ac.uk

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First published: 3 November 2023