BENJAMIN BERNARD

DYNAMIC GAMES | NETWORKS | FINANCIAL ECONOMICS

Education

  • 2011 – 2016

    Ph.D. in Mathematical Finance

    University of Alberta, Edmonton, Canada

    I have studied repeated interactions in continuous time models under the guidance of Prof. Christoph Frei in the Department of Mathematical and Statistical Sciences. Please see the section on my research for more information and find my thesis here.

  • 2009 – 2010

    Master of Science in Mathematics

    ETH Zurich, Switzerland

    I wrote my thesis on the connection of affine processes and Lévy processes under the supervision of Prof. Josef Teichmann. The main focus of my courses was stochastic analysis and mathematical finance.

  • 2006 – 2009

    Bachelor of Science in Mathematics

    ETH Zurich, Switzerland

    Relevant coursework during my degree included probability theory, statistics, risk theory, quantitative risk management, economic theory of financial markets and extreme value theory.

Teaching

  • Fall 2024

    ECON 521 - Games Theory and Economic Analysis

    Whether you are applying for a job, launching a start-up, running for office, or playing poker, the outcome in many situations depends not only on your own decisions but also on those made by others. Game theory examines how to model such interactions formally and which outcomes to expect when everybody takes into account the objectives and decisions of others.

  • Fall 2024

    ECON 711 - Economic Theory – Microeconomics Sequence

    The second quarter of the microeconomics core sequence introduces the core concepts of game theory needed to model and solve games with complete and incomplete information, both in static and in dynamic settings. We study the main solution concepts and understand the underlying assumptions they impose on the rationality and knowledge of the players. Applications range from job applications, procrastination, and politics to social encounters and board games.

  • Fall 2024

    ECON 805 - Advanced Microeconomic Theory I

    Climate agreements, research collaborations, and market competition are examples of long-lasting interactions between strategic decision makers. In addition to maximizing their short-term objective, people in long-run relationships have to take into account how their actions will affect the future of their relationship. Repeated and stochastic games provide the fundamental tools to study intertemporal incentives that support cooperation in such relationships.

Research Papers

  • May 2025

    Bernard, B.

    Continuous-Time Stochastic Games with Imperfect Public Monitoring

    This paper characterizes the set of perfect public equilibrium payoffs, the set of stationary Markov perfect equilibrium payoffs, and a simple class of semi-stationary equilibrium payoffs in continuous-time stochastic games with finitely many states and a publicly observable Brownian signal about past actions. Contrary to many discrete-time methods, the characterization does not rely on a convergence to the stationary distribution ... Download

  • July 2024

    Bernard, B.

    Continuous-Time Games with Imperfect and Abrupt Information.

    This paper studies two-player games in continuous time with imperfect public monitoring, where information may arrive both continuously, governed by a Brownian motion, and discontinuously, according to Poisson processes. For this general class of two-player games, we characterize the equilibrium payoff set via a convergent sequence of differential equations whose solutions ... Download

  • July 2022

    Bernard, B., Capponi, A., and Stiglitz, J.E.

    Bail-Ins and Bail-Outs: Incentives, Connectivity, and Systemic Stability.

    We develop a framework for analyzing how banks can be incentivized to make contributions to a voluntary bail-in and ascertaining the kinds of interbank linkages that are most conducive to a bail-in. A bail-in is possible only when the regulator’s threat to not bail out insolvent banks is credible. Incentives to join a rescue consortium are stronger for banks with a high exposure ... Link, Online Appendix

  • August 2021

    Alsabah, H., Bernard, B., Capponi, A., Iyengar, G., and Sethuraman, J.

    Multiregional Oligopoly with Capacity Constraints

    We develop a model of Cournot competition between capacity-constrained firms that sell a single good to multiple regions. We characterize the unique equilibrium allocation of the good across regions and provide an algorithm to compute it. We show that a reduction in transportation costs by a firm may negatively impact the profit of all firms and reduce consumer surplus if such a firm is capacity constrained... Link

Latex

  • January 2025

    xgames

    A game theory package that places emphasis on user-friendly input and coloring each player's name, actions, and payoffs in a dedicated color for ease of distinction. Information about the game entered within one environment is stored after it is parsed and can be re-used in another environment. Currently still in development. Bug reports are very welcome. Documentation


    Download Find on GitHub

  • June 2024

    assign

    Package for creating problem sets, exams, and question banks with emphasis on ease of use. Single compilation generates three pdfs: the problem set, the solutions, and the grading scheme. Points assigned in the grading scheme are totaled up and displayed on the exam automatically. Problems can be filtered based on labels and/or difficulty. Documentation


    Download

  • May 2022

    fikz

    This is a minimally intrusive package that changes the default overlay behavior of the tikz commands within the beamer document class from the \only to to the `\onslide` behavior. As a consequence, the bounding box of any `tikzpicture` environment is fixed for the entire frame - hence the portmanteau fikz - which prevents images from "jumping around" from slide to slide. Documentation


    Download