International Society of Dynamic Games

Dynamic Games and Applications Seminar

The impacts of environmental policy on industrial allocation: a transboundary pollution dynamic game

March 28, 2024 11:00 AM — 12:00 PM (Montreal time)

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This paper analyzes a dynamic game between two trading regions that face a transboundary pollution problem. We study how the distribution of firms and trade costs affect the optimal emission policy of governments and how this policy would alter the allocation of the industry. The underlying microeconomic behavior is framed within the Economic Geography literature, in particular within the Footloose Capital Model (FCM). The macroeconomic model that arises is a transboundary pollution linear-quadratic dynamic game. We find that if the damage of pollution is high (low), the region with the larger industrial share reduces (increases) its emissions per firm, and that the steady state pollution reaches a minimum (maximum) when firms are fully concentrated in one region. Additionally, the strategic decisions of governments give rise to a new agglomerative force, absent in the FCM, which could lead to industrial activity fully concentrating in a core region.

Dynamic Games and Applications Seminar

Guaranteed cost equilibrium in infinite horizon linear-quadratic differential games

March 7, 2024 11:00 AM — 12:00 PM (Montreal time)

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In this work, we study infinite-horizon linear-quadratic differential games with an output feedback information structure. Our motivation for studying these games arises from their applications in engineering, where players may lack access to complete state information. For example, in a large-scale networked multi-agent system, agents may only possess information about their neighboring agents. In the literature, sufficient conditions for the existence of output feedback Nash equilibria are closely related to solvability of a set of coupled algebraic Riccati equations, with the requirement that these solutions admit certain structural conditions. fulfilling these conditions poses a significant challenge, even in low-dimensional games. Given these limitations, a natural question arises regarding the existence of a broader class of output feedback strategies that adhere to an equilibrium property. Here, ‘broader’ implies that this expanded set of strategies, if it exists, encompasses the output feedback Nash strategies. To address this problem, we introduce the concept of an output feedback guaranteed cost equilibrium. These strategies not only ensure that individual costs remain bounded by a predefined threshold (a design parameter) but also maintain an equilibrium property. The design of these strategies utilizes techniques developed for suboptimal static output feedback controllers and employs linear matrix inequality-based methods for computation.

Dynamic Games and Applications Seminar

A bottom-up approach to the construction of socially optimal discrete choices under congestion

February 29, 2024 11:00 AM — 12:00 PM (Montreal time)

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We consider the problem of N agents having a limited time to decide on a destination choice among a finite number of alternatives D. The agents attempt to minimize collective energy expenditure while favoring motion strategies which limit crowding along their paths in the state space. This can correspond to a situation of crowd evacuation or a group of micro robots distributing themselves on tasks associated to distinct geographic locations. We formulate the problem as a Min linear quadratic optimal control problem with non-positive definite Q matrices accounting for negative costs accruing from decreased crowding. The solution proceeds in three stages, each one improving on the performance of the previous stage: (i) Mapping optimal paths for an arbitrary agent destination assignment; (ii) Mapping optimal paths for fixed fractions of agents assigned to each destination; (iii) Identifying the optimal fraction of agents’ assignments to each destination. The cost function associated with stage (iii) as N goes to infinity is proven to be convex, leads to simplified computations and to epsilon-optimal decentralized control policies when applied for N large.

(with Noureddine Toumi and Jérôme Le Ny).