HEC Montréal, Canada, May 2 - 4, 2011

2011 Optimization Days

HEC Montréal, Canada, 2 — 4 May 2011

Schedule Authors My Schedule

MB9 Théorie des jeux et applications I / Game Theory and Applications I

May 2, 2011 03:30 PM – 05:10 PM

Location: Ordre des CGA du Québec

Chaired by Javier de Frutos

4 Presentations

  • 03:30 PM - 03:55 PM

    Initial Investigations of the Emergence of Coalitions in Mean Field Stochastic Systems

    • Arman C. Kizilkale, presenter, McGill University
    • Peter Caines, GERAD - McGill University

    For noncooperative games the Nash Certainty Equivalence (NCE), or Mean Field (MF) methodology (Huang et al.,2003,2007) provides decentralized strategies which asymptotically yield Nash equilibria. Moreover, an extension of this theory for egoistic agents to populations of altruistic agents (defined with so-called social cost functions) and hence to mixed populations has been carried out in Huang et al. (2010), and Huang (2010) has developed a theory treating populations of egoistic agents and one or more so-called major agents. In this paper we study the emergence of coalitions in a large population LQG problem, where the costs for each minor agent are a convex combination of its own cost and the social cost of the minor agents, and the possibility of minor agents forming coalitions constituting major agents. We investigate the resulting equilibria and provide experimental results on the conditions for the emergence of coalitions.

  • 03:55 PM - 04:20 PM

    Mean Field LQG Games with Mixed Players: The Backward SDE Approach

    • Son Nguyen, presenter, Carleton University
    • Minyi Huang, Carleton University

    We consider mean field LQG games with a major player and a large number of minor players with continuum parameters. The mean field is approximated by a Gaussian process determined by the major player's driven noise, and the decentralized controls of the players are designed based on backward stochastic differential equations. An asymptotic Nash equilibrium property is proved.

  • 04:20 PM - 04:45 PM

    An Evolution Mean Field Equation System of the Consensus Problem

    • Mojtaba Nourian, presenter, McGill University
    • Peter Caines, GERAD - McGill University
    • Roland Malhamé, GERAD - Polytechnique Montréal

    The purpose of this presentation is to study an evolution (i.e., forward in time) mean field equation system of a consensus model. In this model: (i) each agent has a simple stochastic dynamics with inputs directly controlling its state's rate of change, and (ii) each agent seeks to minimize its individual long run average cost function involving a mean field coupling to the states of all other agents. The Evolution Mean Field (EMF) equation system of the continuum (i.e., the population size goes to infinity) version of this model consists of two coupled (forward in time) deterministic PDEs which are also coupled to a (spatially averaged) cost coupling function. In this work the small perturbation stability of the EMF equation system around its stationary equilibrium solution is established.

  • 04:45 PM - 05:10 PM

    Nonlinear Incentive Equilibrium Strategies for a Transboundary Pollution Differential Game

    • Javier de Frutos, presenter, GERAD - Universidad de Valladolid
    • Guiomar Martín-Herrán, GERAD - Universidad de Valladolid

    We characterize non-linear incentive equilibrium strategies for a transboundary pollution differential game. We show that a less stringent concept of cooperation facilitates the credibility of the incentive strategy. We study and compare both open-loop and feedback strategies and we present some numerical illustrations.