On Stable Equilibria

Venue: Povo Zero, via Sommarive 14 (Povo) – Seminar Room "-1"
At: 12:00 a.m.

Speaker:

• Luciano Andreozzi (Università di Trento)    

Abstract:

A large population of individuals play repeatedly a symmetric game and settles on a compact set of Nash equilibria N. Occasionally, they experiment with new strategies and, although initially the new strategies may earn a larger payoff, they cannot coexist stably among themselves. This happens either because they cannot settle on a different Nash equilibrium, or because they cannot enter a stable cycle of invasions.
The population is thus pushed back towards the original set of equilibria N.
In this case we say that the set N is [name] stable. We study the stability properties of [name] stable equilibria under the Best Response and the Replicator Dynamics. A set of NE that is [name] stable is not necessarily asymptotically stable under either dynamics. However, if initially most of the population play pure strategies that appear in N, eventually only these strategies survive, in a combination that belongs to N. In many applications, being [name] stable turns out to be more important than being evolutionarily stable.

Contact person: Andrea Pugliese