Quasi-perfect equilibrium


Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme.
Informally, a player playing by a strategy from a quasi-perfect equilibrium takes observed as well as potential future mistakes of his opponents into account but assumes that he himself will not make a mistake in the future, even if he observes that he has done so in the past.
Quasi-perfect equilibrium is a further refinement of sequential equilibrium. It is itself refined by normal form proper equilibrium.

Mertens' voting game

It has been argued by Jean-François Mertens that quasi-perfect equilibrium is superior to Reinhard Selten's notion of extensive-form trembling hand perfect equilibrium as a quasi-perfect equilibrium is guaranteed to describe admissible behavior. In contrast, for a certain two-player voting game no extensive-form trembling hand perfect equilibrium describes admissible behavior for both players.
The voting game suggested by Mertens may be described as follows:
In the unique quasi-perfect equilibrium for the game, each player votes for himself and, if elected, performs the task correctly. This is also the unique admissible behavior. But in any extensive-form trembling hand perfect equilibrium, at least one of the players believes that
he is at least as likely as the other player to tremble and perform the task incorrectly and hence votes for the other player.
The example illustrates that being a limit of equilibria of perturbed games, an extensive-form trembling hand perfect equilibrium implicitly assumes an agreement between the players about the relative magnitudes of future trembles. It also illustrates that such an assumption may be unwarranted and undesirable.