Selected Research Highlights & Projects

Solutions, computation and stability of solutions to Generalized Nash Games

These are games introduced as far back as the 60's, however are now coming to the forefront from a theoretical as well as an application perspective. These are games where, in addition to a player's payoff being dependent on other players choices, each player's strategy set is also depended upon the other players' choices. They are intimately related to quasi-variational inequality problems. The most well-known and studied class of generalized Nash games is the so called "shared constraints" class, and there are currently various methods (theoretical and numerical) being developed for finding their solution set. 

I am interested in the links between generalized Nash strategies and replicator dynamics in a math biological sense.    

Trainees working on these issues:  B. Benteke (Ph. D.), K. Tarasuk (URA,, M. Sc.)

Dynamics of human behaviour at individual and population levels

Environmental issues are currently at the forefront of our social lives and most policy makers are studying the best policies and strategies towards a decrease in harmful emissions and in consumption of non-renewable resources. Such policies need solid models of individual and population behaviour, since no policy is successful unless it is adopted by a high enough population mass. Thus the question we address here is to quantitatively and qualitatively analyse a population of individuals' decision making process with respect to adoption of green products and technologies.

We study two types of mathematical models of environmental choices in a population, over a given time interval. Each individual is assumed to make both rational decisions(to optimize their well being) and subjective ones (for example decisions based on their personality type and/or their social relations). The first type of model is based on differentiated product market models, partial differential equations and dynamical systems. The other type of model is based on a computational approach, where we simulate the dynamics of a population of individuals with a method called "agent-based", using numerical codes specifically designed for our questions. In a population of consumers making "adopting" decisions based on: product prices, perceived health benefits, global and local social influence, personality type and income, both types of models allow one to compute the adoption level of green products in the population under a wide range of parameters,while allowing for the design of policies that will effectively "move" the population towards a more environmentally friendly behaviour. 

Currently working on these issues: R. Loster (M. Sc. OneHealth)

Math modelling and population health 

I worked for a while on the applications of dynamic games in vaccination behaviour. More specifically, the problem of modelling strategic interactions of various groups within a population under voluntary vaccination policy. We show that vaccination games (both static and dynamic) have solutions, we compute them and study their behaviour under perturbations. The question of accounting for variations in the perceived relative risk of vaccination versus infection across population groups (i.e., the question of treating a population as a heterogeneous entity) has not been formalized in an epidemiological model using tools of variational analysis before. We look as well at how a known vaccination coverage profile in a population can be obtained from the optimal vaccination strategies of each individual population group over a time interval of interest.

Of current interest are combining optimal control (in the form of policy parameters) to control the occurrence and/or stability of Nash strategies in the population; we expanded the games to norms games (a la Axelrod) and to Stackleberg games where the leader is a public health agency and the followers are population groups.  

Last but not least we look at policy programs related to publicly funded vaccination programs as multiyear resource allocation models in Canada. We also use the treasure trove of covid-19 data as pertains to mobility, mask wearing and economic measures in trying to estimate human decision-making vis-a-vis measues to prevent teh spread of infections diseases.

Current students working on these issues: D. Lyver, P. Yue (M. Sc.), Z. Mohammadi (PDF)