Optimization Days 2019

HEC Montréal, May 13-15, 2019


HEC Montréal, 13 — 15 May 2019

Schedule Authors My Schedule

MB4 Game Theory

May 13, 2019 10:30 AM – 12:10 PM

Location: Gérard-Parizeau

Chaired by Margarida Carvalho

4 Presentations

  • 10:30 AM - 10:55 AM

    A game theoretic analysis for community microgrid network

    • Mohamad Aziz, presenter, PhD Candidate, Department of Mathematical and Industrial Engineering, Polytechnique Montreal
    • Hanane Dagdougui, GERAD, Polytechnique Montréal
    • Issmail El Hallaoui, GERAD, Polytechnique Montréal

    Current electricity markets may be better described in terms of an oligopoly than of perfect competition from which they may be rather far. Microgrid, a promising component of the smart grid, will potentially yield a free electricity market. This paper proposes a novel construction for a community microgrid (MG) by deploying a virtual power bank which consists of household storage batteries and mediates the communications between the MG and the macro-grid (MA). Households, representing the distributed energy resources (DER) and the demand side, are considered the MG prosumers (i.e. they are the consumers and the potential energy producers). In this paper, Nash Equilibrium strategies which minimize a linear combination of the households' energy generation cost, energy consumption cost and revenue of sold energy are found via an application of mean field control theory (MFG). The decentralized community microgrid optimization (MGO) problem via mean field control is configured using a flat rate macrogrid pricing mechanisms. Computational investigations of the decentralized MGO problem via MFG are presented for a constructed community MG in Quebec, Canada.

    keywords: Smart Grid, Microgrid, Optimization, Decentralized Control, Decentralized Mean Field Game Theory, Dynamical Game, Stochastic Control.

  • 10:55 AM - 11:20 AM

    Impact of a leader-follower equilibrium concept on the stability of environmental agreement

    • Samar Garrab, presenter, Royal Military college of Canada

    We study in this paper the impact of the leader-follower equilibrium concept on the stability of international environmental agreements. In an infinite-horizon dynamic game, we assume that signatories hold the leader role and decide first about their emission strategies while non-signatories are followers.

    Keywords: dynamic games; environmental agreements; leader-follower.

  • 11:20 AM - 11:45 AM

    Is it time to intervene? An impulse control approach to dynamic games

    • Utsav Sadana, presenter, GERAD, HEC Montreal
    • Puduru Viswanadha Reddy, Indian Institute of Technology - Madras, India
    • Georges Zaccour, Chair in Game Theory and Management, GERAD and HEC Montréal

    In this paper, we introduce a class of two player non-zero-sum dynamic games (DG) where one player uses continuous control while the other player uses impulse control. We determine the necessary and sufficient conditions for the existence of open loop Nash equilibrium. For linear state DG, we obtain analytical solutions.

    Keywords: impulse control, dynamic games, Nash equilibrium

  • 11:45 AM - 12:10 PM

    When Nash meets Stackelberg

    • Felipe Feijoo, PUCV, Chile
    • Andrea Lodi, Polytechnique Montreal
    • Sriram Sankaranarayanan, presenter, Polytechnique Montreal

    We provide an algorithm to compute a mixed-strategy Nash equilibria of a Nash game where each player's (or leader's) pay off is given as a bilevel linear program. This leads to a situation where the leaders not only play a Nash game with other leaders but also a Stackelberg game with their own follower(s). The algorithm exploits the polyhedral structure in the game and our ability to solve mixed-integer linear program fast. We then use this model to solve for equilibrium in a Nash game among countries (leaders) where each country also plays a Stackelberg game with their indigenous industries (followers).