'Quantile-Dependent Mean Field Games with Applications to Early-Stage Venture Investments', a seminar by Professor Michele Breton (HEC Montreal)

Quantile-Dependent Mean Field Games with Applications to Early-Stage Venture Investments

By Professor Michele Breton from HEC Montreal

Abstract:

Mean-field game models involve the distribution of states or controls across the agent population, which in linear-quadratic settings typically reduces to the inclusion of the mean value of the distribution. We address a class of quantilized models, which rather include quantiles of the state distribution. This class of models is a generalization of the classical linear-quadratic setting, where the quantile level is set to 0.5.

Ranking quantilized games model a competition between homogeneous agents, set by a coordinator who aims to select a certain proportion of top ranking agents at the end of the time horizon. The proportion is predetermined and announced by the coordinator before the competition begins, and the performance of the agents is evaluated at the terminal time. The threshold for success is determined based on the collective performance of agents.

We propose an application to early-stage venture investments, where a venture capital firm sets a threshold for success, which depends on the performance of a large pool of startup companies competing for funding over a finite horizon. We provide two formulations for this competition (target-based and threshold-based, where the target-based formulation can be solved analytically. Through numerical experiments, we show that this analytical solution provides a very good approximation for the threshold-based formulation.

About the speaker:

Michèle Breton is a Professor in the Department of Decision Sciences at HEC Montréal in Québec, Canada.

Other titles:

• Director of the Department of Decision Sciences
• Holder of the Research Professorship in Dynamic Optimization
• Fellow of the Royal Society of Canada
• Member of the Group for Research on Decision Analysis (GERAD)

Education:

• M. Ing. (recherche opérationnelle), Polytechnique
• Ph. D. (informatique), Université de Montréal

Expertise:

• Game theory
• Operations research
• Decision analysis
• Mathematical models in finance and in energy