International Society of Dynamic Games

Dynamic Games and Applications Seminar

Stable partitions in networks with the costs dependent on neighborhood composition

Feb 5, 2026 11:00 AM — 12:00 PM (Montreal time)

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We study a discrete-time, infinite-horizon process of partition formation. We introduce two cost functions for maintaining connections within a network, allowing the cost of a link between two players to depend on the composition of each player’s neighborhood. Stable partitions are characterized when players interact on a star network, a complete network, and on balanced complete bipartite networks. Finally, we apply the model to Zachary’s karate club network, providing an explanation for why two specific individuals can be viewed as group leaders. Numerical simulations on random networks further illustrate the process and underscore the theoretical intractability of the problem. (With Elena Parilina)

Dynamic Games and Applications Seminar

Will Generative AI Empower or Replace Us? Task Creation, Automation, and the Wage-Productivity Gap

Jan 29, 2026 11:00 AM — 12:00 PM (Montreal time)

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This paper analyzes whether generative artificial intelligence (AI) empowers or replaces workers by endogenizing the sequencing of innovation between task creation and automation. We develop a dynamic model in which firms invest in task creation, which expands labor-performed activities, and automation, which reallocates existing tasks to machines. Firms optimally switch from task creation to automation at a unique and irreversible time. This sequencing generates rising wages early on and declining wages later, while productivity increases throughout, producing an endogenous wage–productivity gap. We further derive a welfare-based, stage-contingent innovation policy, showing that uniform interventions are inefficient.

Dynamic Games and Applications Seminar

Non-smooth and discontinuous Markov Perfect Nash Equilibrium in differential games

Jan 22, 2026 11:00 AM — 12:00 PM (Montreal time)

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We establish necessary and sufficient conditions that characterize the Markov Perfect Nash Equilibrium (MPNE) in differential games, specifically when the equilibrium may be only piecewise smooth with respect to the state variable. Our approach follows the classical framework presented in [1] and its references, which is based on constructing an admissible set of discontinuities for the strategies. We connect this concept with the well-known Rankine-Hugoniot jump conditions, which are commonly used in fluid dynamics to study weak solutions of the equations that define the problem. Under appropriate strict concavity assumptions, the entropy condition, as applied to the weak solutions of the fluid dynamic equations, allows us to identify the unique MPNE from a large number of candidate profiles that are also weak solutions. We illustrate our findings using a finite-horizon differential game involving the non-cooperative management of a non-renewable resource. We demonstrate how imposing a non-concave utility function at the final time leads to a discontinuous MPNE.