Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible...

A component of Nash equilibria is (dynamically) potentially stable if there exists an evolutionary selection dynamics from a broad class for which the component is asymptotically stable. A necessary condition for potential stability is that the component's index agrees with its Euler...

We show that in long repeated games- or in infinitely repeated games with discount rate close to one- payoffs corresponding to evolutionary stable sets are asymptotically efficient, as intuition suggests. Actions played at the beginning of the game are used as messages that allow players to...