# LSV Seminar

The LSV seminar takes place on Tuesday at 11:00 AM. The usual location is the conference room at Pavillon des Jardins (venue).
If you wish to be informed by e-mail about upcoming seminars, please contact Stéphane Le Roux and Matthias Fuegger.

The seminar is open to public and does not require any form of registration.

## Seminar

### The compact-overt duality and the existence of equilibria in infinite-duration games

- Date
- 25.06.2019, 11:00
- Place
- Pavillon des Jardins
- Speaker
- Arno Pauly (Swansea University)

A useful yet often overlooked characterization of compact sets is that universal quantification over them preserves open predicates. In a constructive setting, the dual notion -- that of a set such that existential quantification preserves open predicates -- is non-trivial, and dubbed overtness. The first part of this talk will be a gentle introduction to these concepts in the framework of synthetic topology. As an application, we turn to infinite-duration games. In general, we shall see that if strategy sets are compact and overt, and preference relations are open, then the set of games without a Nash equilibrium is open. Since in most set-ups the finite duration games are dense inside the infinite-duration games, we can thus lift existence-results for equilibria from the former to the latter. By modifying the preferences, we can consider other equilibrium notions such as subgame-perfect equilibria as a special case. Handling more complex notions such as trembling-hand equilibria requires an additional small argument, but their existence is still readily established using our framework.