Here is an experiment that as far as I know has not been done. (Please correct me if I am wrong.) Offer contestants the choice of two raffles. Raffle A pays the winner $1000, Raffle B pays the winner $1000+x where x is a positive number. Contestants must pick one of the raffles and can buy at most one raffle ticket. They choose simultaneously. There will be one winner from each raffle and the winners will be determined by random draw.
In equilibrium the expected payoff in the two raffles should be equalized. This means that more people should enter raffle B to compete away the extra $x prize money. My hypothesis is that in fact too many people will enter raffle B so that raffle A will have a higher expected payoff. I am thinking that the contestants will inusfficiently account for the strategic effect of free entry and will naively assume that B is the better choice. And I believe this effect will be large even when x is very small.
If this is true then it has important consequences for markets. Suppose two job market candidates are almost equally qualified but candidate A is a little better than candidate B. Candidate A will get too many interviews and candidate B will get too few. Candidate B’s slight disadvantage will be amplified by the market and will go too often unemployed.
In the economics job market for new PhD’s, economics departments are often asked by potential employers for rankings of their candidates. Departments are often unwilling to give more than coarse rankings and I believe that the effect I describe is the reason.
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October 29, 2009 at 6:25 pm
Anonymous
overshooting?
October 29, 2009 at 7:49 pm
rd
damn you’re good
October 29, 2009 at 7:57 pm
rd
actually maybe this idea is similar to what’s shown in this paper-
https://editorialexpress.com/cgi-bin/conference/download.cgi?db_name=NASM2009&paper_id=1200
-that people overreact to small changes in rankings (?)
October 29, 2009 at 8:39 pm
jeff
thank you for the reference.
October 30, 2009 at 12:45 am
Lones Smith
Jeff,
Great minds — or minds interested in watersports — think alike, or alike in question, but different in conjecture. I set a grad student to work on this about two or three years ago asking if this very effect was present in Powerball and Mega Millions lotteries. As you might know, these are rollover lotteries. Occasionally the prize grows to hundreds of millions of dollars.
http://www.megamillions.com/winners/winner.asp?bioID=3&startItem=1
So the natural question is do so many people enter that the expected payoff holds constant? Honestly, that was my conjecture. But it failed for a simple reason — albeit that is absent from your one-on-one thought experiment. Namely, new people are drawn into playing the lotto. These people are previously (at lower payouts) uninterested in playing — and need to be coaxed with higher odds. In fact, this is clearly true in the data — a convex shape. Cool, I thought, and ex post clear. I might have had a paper out of it had this been a NWU student with initiative, sigh.
Surf’s up! – Lones
November 2, 2009 at 2:26 pm
JD
Isn’t this a symmetric process for applicants, too? Do applicants systematically overshoot and spend too much time and energy applying for top jobs, seeking a high payoff and underestimating the number of other applicants for those posts?
What happens when applicants overshoot AND firms overshoot?
Applicants apply to more ‘good’ jobs than they should and fewer ‘appropriate’ matches.
Firms select more ‘overqualified’ applicants than they should and neglect ‘appropriate’ matches.
A firm of quality level X would see a distribution of applicants with a mean quality less than X, because applicants with quality X would be applying at firms with quality greater than X.
So if firms tend to pick only candidates from the top of the distribution, they would be inadvertently correcting for the unrealistic optimism of applicants. If firms and applicants both “insufficiently account for the strategic effect of free entry” to the same degree, then the outcome could still be optimal, except for the wasted application and interview costs.