International Society of Dynamic Games

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.

Dynamic Games and Applications Seminar

Ultimatum game: Regret or fairness

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

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In the ultimatum game, the challenge is to explain why responders reject non-zero offers thereby defying classical rationality. Fairness and related concepts have been among the main explanations so far. Here, the ultimatum game is reformulated based on probabilistic lotteries, enabling other decision-making tools to be applied to this problem. We explain the rejection behavior via the following principle: if the responder regrets less about losing the offer than the proposer regrets not offering a better option, the offer is rejected. We show that several experimental results normally prescribed to fairness can be given an alternative explanation. We also propose experiments that can distinguish these two scenarios. (With Armen Allahverdyan and Lida Aleksanyan).

Dynamic Games and Applications Seminar

Discrimination in games

Dec 4, 2025 11:00 AM — 12:00 PM (Montreal time)

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We consider a finite population formed by different types of individuals. Players observe the type of their opponent but do not know their own type. This assumption is discussed in different contexts, such as biology, and medecine. The question that we address is whether in such a symmetric environment a discriminating norm may arise.