Mathematical Finance & Financial Data Science Seminar

The Algorithmic Learning Equations: Evolving Strategies in Dynamic Games

Location: Online Zoom access provided to registrants

Date: Tuesday, November 29, 2022, 5:30 p.m.

Synopsis:

We introduce the algorithmic learning equations, a set of ordinary differential equations which characterizes the finite-time and asymptotic behavior of the stochastic interaction between state-dependent learning algorithms in dynamic games. Our framework allows for a variety of information and memory structures, including noisy, perfect, private, and public monitoring and for the possibility that players use distinct learning algorithms. We prove that play converges to a correlated equilibrium for a family of algorithms under correlated private signals. Finally, we apply our methodology in a repeated $2 \times 2$ prisoner's dilemma game with perfect monitoring. We show that algorithms can learn a reward-punishment mechanism to sustain tacit collusion. Additionally, we find that algorithms can also learn to coordinate in cycles of cooperation and defection.

Speaker Bio:

José Penalva is Assiociate Professor of Finance at the Business Department of the Universidad Carlos III. He has an economics doctorate from the University of California, Los Angeles (UCLA) since 1997. He currently teaches Information in Markets and Market Microstructure, and Financial Mathematics.

His research interests are: the economics of information with a special emphasis on market microstructure, financial applications, law and economics, and risk insurance. His publications include journals of international prestige such as Econometrica, Journal of Banking and Finance, Applied Mathematical Finance, Quarterly Journal of Finance, Review of Economic Dynamics and the Journal of Risk and Insurance. He gives presentations of his research at prestigious international conferences such as the European Group of Risk and Insurance Economists (EGRIE), the European Economic Association, the European Finance Association, and the European Econometric Society Meeting, among others. He has also participated in several edited books, and has co-authored (with Alvaro Cartea and Sebastian Jaimungal) the book "Algorithmic and High-frequency Trading" (Cambridge University Press, 2015)

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