International Society of Dynamic Games

Dynamic Games and Applications Seminar

A Differential Game Approach for the Opioid Epidemic

Nov 21, 2024 11:00 AM — 12:00 PM

Zoom webinar link

Under the continuous evolution of the opioid epidemic in the US, the recent increase in addiction as well as overdose deaths due to synthetic opioids, despite increased regulations on prescription practices, warrant a more long-term forward-looking approach incorporating the strategic responses of the other stakeholders. In this work, we model the interactions between the multiple stakeholders, as a three player non-cooperative differential game between the government, health-care providers and the illicit drug providers. The state dynamics for our differential game approach is built upon a recent data-driven epidemiological model on the opioid addiction in Tennessee, extending it to include the effects of the controls or strategies of the three players. In this paper, we compute the open loop Nash Equilibrium using the minimum principle and analyze the equilibrium control strategies of the three players and compare the optimal state trajectory of the system with that of the uncontrolled system.

Dynamic Games and Applications Seminar

Comparative Dynamics in a Dynamic Oligopoly Model of Capital Accumulation

Nov 14, 2024 11:00 AM — 12:00 PM

Zoom webinar link

We revisit the generalized finite horizon dynamic oligopoly model of capital accumulation in a differential game setting and use the Oniki’s variational method to investigate the comparative dynamics of a symmetric Open-loop Nash Equilibria (OLNE) of the game with respect to several variables. We are able to trace the entire path of the comparative dynamics of these variables over the time horizon and we are thus able to determine the dynamics of the effects of changes in the parameters on the symmetric OLNE. An immediate implication of our derived comparative dynamics is that they give sharper envelope predictions than results in the existing literature. For example, we show that the initial value of a firm’s own costate variable underestimates the shadow value of the initial capital stock.

Dynamic Games and Applications Seminar

Subsidizing a New Technology: An Impulse Stackelberg Game Approach

Oct 31, 2024 11:00 AM — 12:00 PM (Montreal SUMMER time)

Zoom webinar link

Governments are motivated to subsidize profit-driven firms that manufacture zero-emission vehicles to ensure they become price-competitive. This paper introduces a dynamic Stackelberg game to determine the government’s optimal subsidy strategy for zero-emission vehicles, taking into account the pricing decisions of a profit-maximizing firm. While firms have the flexibility to change prices continuously, subsidies are adjusted at specific time intervals. This is captured in our game formulation by using impulse controls for discrete-time interventions. We provide a verification theorem to characterize the Feedback Stackelberg equilibrium and illustrate our results with numerical experiments. (with Georges Zaccour)