HEC Montréal, Canada, May 2  4, 2011
2011 Optimization Days
HEC Montréal, Canada, 2 — 4 May 2011
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
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 socalled 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 socalled 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
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
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
We characterize nonlinear 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 openloop and feedback strategies and we present some numerical illustrations.