| Quasi-perfect Equilibrium | |
|---|---|
| Solution concept ingame theory | |
| Relationship | |
| Subset of | Sequential equilibrium,normal-form trembling hand perfect equilibrium |
| Significance | |
| Proposed by | Eric van Damme |
| Used for | Extensive form games |
| Example | Mertens' voting game |
Quasi-perfect equilibrium is a refinement ofNash Equilibrium forextensive form games due toEric van Damme.[1]
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 ofsequential equilibrium. It is itself refined by normal formproper equilibrium.
It has been argued byJean-François Mertens[2] that quasi-perfect equilibrium is superior toReinhard Selten's notion ofextensive-form trembling hand perfect equilibrium as a quasi-perfect equilibrium is guaranteed to describeadmissible behavior. In contrast, for a certain two-player voting gamenoextensive-form trembling hand perfect equilibrium describesadmissible 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 uniqueadmissible behavior. But in anyextensive-form trembling hand perfect equilibrium, at least one of the players believes thathe 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, anextensive-form trembling hand perfect equilibrium implicitly assumes anagreement between the players about the relative magnitudes of future trembles. It also illustrates that such an assumption may be unwarranted and undesirable.
