Description
In 1950, Nash published a very influential two-page paper proving the existence of Nash equilibria for any finite game. The proof uses an elegant application of the Kakutani fixed-point theorem from the field of topology. It has, however, been noted that in some cases the Nash equilibrium fails to predict the most beneficial outcome for all players. To address this, generalizations of Nash equilibria such as correlated and dependency equilibria were introduced. This talk explores these notions of equilibria and presents methods to compute them from a nonlinear algebraic perspective, offering insights into their computational challenges.
