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The Séminaire parisien de Théorie des Jeux is an open, inter-institutional, multi-disciplined seminar which covers all fields of game theory. It takes place on Monday from 11:00 to 12:00 am at Institut Henri Poincaré, 11 rue Pierre et Marie Curie, Paris 5ème. MAP

You will find the program for the current academic year on the page 2026/2027 and the program for past years on the page Archives.

The junior seminar welcomes PhD students in game theory to present their work.  You will find the program for the current academic year on the page Junior Seminar 2026/2027.

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Next seminar:  

September 28, 2026 (room Maryam Mirzakhani 201): 

Abraham Neyman (Hebrew University of Jerusalem)

Title : Continuous Selections of Nash ε-Equilibria: What Continuity Costs?

Abstract : Fix a finite two-player strategic-game form in which each player has at least two pure strategies. Let $\mathcal{G}$ be the real vector space of all real-valued strategic games on this form, and let $\mathcal{G}^0 \subseteq \mathcal{G}$ be the linear subspace of zero-sum games. On $\mathcal{G}^0$, for every $\varepsilon > 0$, $\varepsilon$-optimal strategies can be selected Lipschitz continuously as the payoff function varies. We show that on all of $\mathcal{G}$ this fails as strongly as possible: for any $\varepsilon > 0$, there is no continuous map assigning to each game a Nash $\varepsilon$-equilibrium. 

For a set $Y$ of games, the cost of continuity on $Y$ is the infimum of those $\varepsilon > 0$ for which $Y$ admits a continuous selection of Nash $\varepsilon$-equilibria. The obstruction is present already in the smallest setting, and there the cost can be computed exactly: for symmetric two-player binary-action games with payoffs in [0, 1], the maximal cost is 1/17 over line segments and 1/8 over paths, and the cost over the whole cube is 1/8 as well, though the infimum defining it is not attained there. Since regrets scale with the payoffs, these are relative costs—over families with payoffs in [0, K] they become K/17 and K/8, and on the entire space of games the cost is infinite. The cost is higher with more players: for symmetric anonymous n-player binary-action games the maximal cost over line segments of games with payoffs in [0, 1] is asymptotically at least 1/6.

A parallel contrast holds for stochastic games, with discounted payoffs normalized as usual. For every finite two-player zero-sum stochastic game and every $\varepsilon > 0$, $\varepsilon$-optimal strategies of the $\lambda$-discounted game can be selected Lipschitz continuously in $\lambda \in (0, 1)$. By contrast, there is a finite two-player stochastic game and an $\varepsilon > 0$ for which no continuous map $\lambda \mapsto \sigma_\lambda$ selects an $\varepsilon$-equilibrium of the $\lambda$-discounted game; such a game can be found already among symmetric two-player binary-action absorbing games with payoffs in [0, 1], and for the one we construct the cost of continuity is 1/17.

This separates ordinary Nash equilibrium from sunspot, and more generally mediated, equilibrium notions. In both the strategic and the stochastic setting the dividing line is convexity: sets of $\varepsilon$-optimal strategies, and of mediated ε-equilibria, are convex, so strategy choices can be averaged with Lipschitz continuously varying weights, and a Lipschitz continuous selection exists for every ε > 0; sets of Nash ε-equilibria are not convex, and the results above show that no other route to a global continuous selection is available either. The separation also shows that local robustness of ordinary Nash equilibria with respect to the players' evaluation of the future does not imply a global continuous selection.

Organizers

Michael Greinecker (ENS Paris-Saclay), michael(dot)greinecker(at)ens(minus)paris(minus)saclay(dot)fr

Frédéric Koessler (CNRS, HEC Paris), frederic.koessler[at]gmail[dot]com

Maël Le Treust  (CNRS,  IRISA Rennes), mael.le-treust[at]cnrs[dot]fr

Christina Pawlowitsch (Lemma, Université Paris-Panthéon-Assas), christina.pawlowitsch[at]assas-universite[dot]fr

Yannick Viossat (CEREMADE, PSL), viossat[at]ceremade[dot]dauphine[dot]fr

Former organizers

Joseph Abdou; Bernard De Meyer; Françoise Forges; Olivier Gossner;  Frederic Koessler; Marie Laclau; Rida Laraki; Chantal Marlats; Lucie Ménager; Vianney Perchet; Jérôme Renault; Dinah Rosenberg; Sylvain Sorin; Tristan Tomala; Xavier Venel; Nicolas Vieille; Guillaume Vigeral; Bruno Ziliotto

Past conference: 30 Years of Game Theory at Institut Henri Poincaré, October 06-10, 2025, Paris.