Pooling equilibrium
Every type ends up behaving the same way, so watching what someone does tells you nothing about which type they are.
Often misread asAssuming that once a separating equilibrium has been found, the pooling one is ruled out, so only a single answer is looked for.
How to see it
Everyone does the same thing, so the action says nothing
In a pooling equilibrium every type of informed player takes the same action, so the uninformed side learns nothing from watching and keeps the beliefs it started with. What holds it together is what everyone expects would be thought of someone who did something different: if stepping out of line would be read badly, nobody steps out.
The checkBoth can be equilibria of the same game at the same time. Choosing between them requires an argument about beliefs off the equilibrium path, not a comparison of payoffs on it.
Try itTake a candidate pooling equilibrium and ask what the uninformed party would have to believe about anyone who deviated, for the deviation to be unattractive. If no belief makes it unattractive, the pooling collapses.
Games that show it
Know these first
Easily confused with
Sources
- Spence, M. (1973). Quarterly Journal of Economics 87(3), 355-374.
- Fudenberg, D. & Tirole, J. (1991). MIT Press.