International Society of Dynamic Games

Dynamic Games and Applications Seminar

Differential games of public investment

Feb 6, 2025   11:00 AM — 12:00 PM (Montreal time)

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We define a differential game of dynamic public investment with a discontinuous Markovian strategy space. The best response correspondence for the game is well-behaved: best responses exist and uniquely map almost all profiles of opponents’ strategies back to the strategy space. Our chosen strategy space thus makes the differential game well-formed, resolving a long-standing open problem and allowing the analysis of a wider class of differential games and Markov-perfect equilibria. We provide a ‘cookbook’ necessary and sufficient condition for constructing the best response, and demonstrate its use with a canonical model of non-cooperative mitigation of climate change. Our approach provides novel, economically important results: we obtain the entire set of symmetric Markov-perfect Nash equilibria, and demonstrate that the best equilibria can yield a substantial welfare improvement over the equilibrium which previous literature has focused on. Our methods do not require specific functional forms.

Dynamic Games and Applications Seminar

Nonlinear Strategies in Symmetrical Two-person Scalar LQ

Jan 30, 2025   11:00 AM — 12:00 PM (Montreal time)

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Since the often quoted article Tsutsui and Mino 1990, there has been some confusion over what this article proves. Rowat, 2007, uses the same method plus Dockner et al 2000 on another example. We explain that what is proved by Tsutsui and Mino is not what they claim, and what is proved by Rowat is misnamed as a perfect equilibrium. However, Rowat’s example can easily be saved as noted by several authors. Using a more general model, we discuss which parameter values yield his results and we give an explicit and simpler derivation concerning his original piecewise linear strategies.

Dynamic Games and Applications Seminar

ShapG: new feature importance method based on the Shapley value

Jan 23, 2025   11:00 AM — 12:00 PM (Montreal time)

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With wide application of Artificial Intelligence (AI), it has become particularly important to make decisions of AI systems explainable and transparent. In this paper, we proposed a new Explainable Artificial Intelligence (XAI) method called ShapG (Explanations based on Shapley value for Graphs) for measuring feature importance. ShapG is a model-agnostic global explanation method. At the first stage, it defines an undirected graph based on the dataset, where nodes represent features and edges are added based on calculation of correlation coefficients between features. At the second stage, it calculates an approximated Shapley value by sampling the data taking into account this graph structure. The sampling approach of ShapG allows to calculate the importance of features efficiently, i.e. to reduce computational complexity. Comparison of ShapG with other existing XAI methods shows that it provides more accurate explanations for two examined datasets. We also compared other XAI methods developed based on cooperative game theory with ShapG in running time, and the results show that ShapG exhibits obvious advantages in its running time, which further proves efficiency of ShapG. In addition, extensive experiments demonstrate a wide range of applicability of the ShapG method for explaining complex models. We find ShapG an important tool in improving explainability and transparency of AI systems and believe it can be widely used in various fields. (Joint work with Chi Zhao and Jing Liu.)