So the
benchmark is represented by the situation where no signaling takes place and employers—not
being able to distinguish between more productive and less productive applicants and not having
any elements on which to base a guess—offer the same wage to every applicant, equal to the
average productivity. Call this the non-signaling equilibrium. In a signaling equilibrium (where
employers’ beliefs are confirmed, since less productive people do not invest in education, while
the more productive do) everybody may be worse off than in the non-signaling equilibrium. This
occurs if the wage offered to the non-educated is lower than the average productivity (= wage
offered to everybody in the non-signaling equilibrium) and that offered to the educated people is
higher, but becomes lower (than the average productivity) once the costs of acquiring education
are subtracted. The possible Pareto inefficiency of signaling equilibria is a strong result and a
worrying one: it means that society is wasting resources in the production of education.
However, it is not per se enough to conclude that education (i.e. the signaling activity) should be
eliminated. The result is not that, in general, elimination of the signaling activity leads to a
Pareto improvement: Spence simply pointed out that this is a possibility.
So in theory it seems quite possible that privacy is a sort of coordination mechanism for avoiding bad signaling equilibria. Whether or not it actually is, I’m not sure. That seems to require empirical investigation and I’m not aware of such research.
I get a 404 for the paper. The part you quoted says “maybe this might happen” but doesn’t give an economic argument that it could happen, it just says “maybe employers don’t pay people enough for it to be worth it”. Is there somewhere where the argument is actually made?
It looks like the code that turns a URL into a link made the colon into part of the link. I removed it so the link should work now. The argument should be in the PDF. Basically you just solve the game assuming the ability to signal and compare that to the game where signaling isn’t possible, and see that the signaling equilibrium makes everyone worse off (in that particular game).
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).
To support this, there are results from economics / game theory showing that signaling equilibria can be worse than non-signaling equilibria (in the sense of Pareto inefficiency). Quoting one example from http://faculty.econ.ucdavis.edu/faculty/bonanno/teaching/200C/Signaling.pdf
So in theory it seems quite possible that privacy is a sort of coordination mechanism for avoiding bad signaling equilibria. Whether or not it actually is, I’m not sure. That seems to require empirical investigation and I’m not aware of such research.
I get a 404 for the paper. The part you quoted says “maybe this might happen” but doesn’t give an economic argument that it could happen, it just says “maybe employers don’t pay people enough for it to be worth it”. Is there somewhere where the argument is actually made?
It looks like the code that turns a URL into a link made the colon into part of the link. I removed it so the link should work now. The argument should be in the PDF. Basically you just solve the game assuming the ability to signal and compare that to the game where signaling isn’t possible, and see that the signaling equilibrium makes everyone worse off (in that particular game).
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).