Decision, Algorithms and Geometry

Joint seminar of the Optimization team of CERMICS (Ecole des Ponts
Paristech) and the Tropical team (INRIA Saclay & CMAP, Ecole

Forthcoming sessions

Guillaume Vigeral (Ceremade, Paris Dauphine)

April 8th, 10:30, Online

Structure of the sets of Nash equilibria of finite games; applications
to the complexity of some decision problems in game theory

The set of Nash equilibrium payoffs of a finite game is always non
empty, compact and semialgebraic. We show that, for 3 players or more,
the reverse also holds: given E a subset of R^N that is non empty,
compact and semialgebraic, one constructs a finite N player game such
that E is its set of equilibrium payoffs. Related results also holds
when one consider only games with integral payoffs, or when the focus is
on equilibria instead of equilibrium payoffs.
We apply this result to understand the complexity class of some natural
decision problems on finite games.