OK, looking at the argument, I think it makes sense that signalling equilibria can potentially be Pareto-worse than non-signalling equilibria, as they can have more of a “market for lemons” problem. Worth noting that not all equilibria in the game-with-signalling are worse than non-signalling equilibria (I think “no one gets education, everyone gets paid average productivity” is still a Nash equilibrium), it’s just that signalling enables additional equilibria, some of which are bad.
OK, looking at the argument, I think it makes sense that signalling equilibria can potentially be Pareto-worse than non-signalling equilibria, as they can have more of a “market for lemons” problem.
Not sure what the connection to “market for lemons” is. Can you explain more (if it seems important)?
(I think “no one gets education, everyone gets paid average productivity” is still a Nash equilibrium)
I agree that is still a Nash equilibrium and I think even a Perfect Bayesian Equilibrium, but
there may be a stronger formal equilibrium concept that rules it out? (It’s been a while since I studied all those equilibrium refinements so I can’t tell you which off the top of my head.)
I think under Perfect Bayesian Equilibrium, off-the-play-path nodes formally happen with probability 0 and the players are allowed to update in an arbitrary way on those nodes, including not update at all. But intuitively if someone does deviate from the proposed equilibrium strategy and get some education, it seems implausible that employers don’t update towards them being type H and therefore offer them a higher salary.
Not sure what the connection to “market for lemons” is.
People who haven’t gotten an education are, on average, unproductive, since productive people have a better alternative to not getting an education (namely, getting an education). Similarly, in a market for lemons, cars on the market are, on average, low-quality, since people with high-quality cars have a better alternative to putting them on an open market (namely, continuing to use the car, or selling it in a higher-trust market).
I agree that is still a Nash equilibrium and I think even a Perfect Bayesian Equilibrium, but there may be a stronger formal equilibrium concept that rules it out?
It’s possible, I don’t know the formal stronger equilibrium concepts though.
Now that I think about it, there are even simpler cases of more-available information making Nash equilibria worse. In any finite iterated prisoner’s dilemma with known horizon, the only Nash equilibrium is to always defect. But, in a finite iterated prisoner’s dilemma with unknown geometrically-distributed horizon (sufficiently far away in expectation), there are Nash equilibria that generate mutual cooperation (due to folk theorems).
OK, looking at the argument, I think it makes sense that signalling equilibria can potentially be Pareto-worse than non-signalling equilibria, as they can have more of a “market for lemons” problem. Worth noting that not all equilibria in the game-with-signalling are worse than non-signalling equilibria (I think “no one gets education, everyone gets paid average productivity” is still a Nash equilibrium), it’s just that signalling enables additional equilibria, some of which are bad.
Not sure what the connection to “market for lemons” is. Can you explain more (if it seems important)?
I agree that is still a Nash equilibrium and I think even a Perfect Bayesian Equilibrium, but there may be a stronger formal equilibrium concept that rules it out? (It’s been a while since I studied all those equilibrium refinements so I can’t tell you which off the top of my head.)
I think under Perfect Bayesian Equilibrium, off-the-play-path nodes formally happen with probability 0 and the players are allowed to update in an arbitrary way on those nodes, including not update at all. But intuitively if someone does deviate from the proposed equilibrium strategy and get some education, it seems implausible that employers don’t update towards them being type H and therefore offer them a higher salary.
People who haven’t gotten an education are, on average, unproductive, since productive people have a better alternative to not getting an education (namely, getting an education). Similarly, in a market for lemons, cars on the market are, on average, low-quality, since people with high-quality cars have a better alternative to putting them on an open market (namely, continuing to use the car, or selling it in a higher-trust market).
It’s possible, I don’t know the formal stronger equilibrium concepts though.
Now that I think about it, there are even simpler cases of more-available information making Nash equilibria worse. In any finite iterated prisoner’s dilemma with known horizon, the only Nash equilibrium is to always defect. But, in a finite iterated prisoner’s dilemma with unknown geometrically-distributed horizon (sufficiently far away in expectation), there are Nash equilibria that generate mutual cooperation (due to folk theorems).