Proper equilibrium
A refinement in which players still make mistakes, but a mistake that costs more is made very much less often than one that costs less.
Often misread asTreating it as a stricter version of trembling hand perfection for some unspecified reason, rather than seeing that the entire extra strictness comes from ordering the trembles by how costly they are.
How to see it
Expensive mistakes are made far more rarely
Trembling hand perfection lets players slip but does not rank the slips, so a catastrophic error is as likely as a trivial one. Proper equilibrium says that if a player is going to err, they err with some care, and a mistake that costs more is made very much less often than one that costs little.
The checkBoth allow trembles. Proper adds only that a more costly mistake occurs with vanishingly smaller probability than a cheaper one, and every extra bite of the concept comes from that.
Try itGive a player two possible errors, one costing a pound and one costing a hundred. Under trembling hand both may occur at one in a thousand. Under properness, say which rate must shrink faster, then say which opposing strategy that change rescues or kills.
Know these first
Easily confused with
Sources
- Myerson, R. B. (1978). International Journal of Game Theory 7(2), 73-80.
- Myerson, R. (1991). Harvard University Press.
- Fudenberg, D. & Tirole, J. (1991). MIT Press.