# 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.

## Past Seminars

### The Complexity of Nash Equilibria in Stochastic Games

- Date
- Tuesday, December 08 2009 at 11:00AM
- Place
- Salle de Conférence (Pavillon des Jardins)
- Speaker
- Michael Ummels (RWTH Aachen)

We analyse the computational complexity of finding Nash equilibria in
simple stochastic multiplayer games. We show that restricting the
search space to equilibria whose payoffs fall into a certain interval
may lead to undecidability. In particular, we prove that the following
problem is undecidable: Given a game G, does there exist a
pure-strategy Nash equilibrium of G where player 0 wins with
probability 1. Moreover, this problem remains undecidable if it is
restricted to strategies with (unbounded) finite memory. However, if
mixed strategies are allowed, decidability remains an open problem.
One way to obtain a provably decidable variant of the problem is
restricting the strategies to be positional or stationary. For the
complexity of these two problems, we obtain a common lower bound of NP
and upper bounds of NP and PSPACE respectively.