poly: How to buy shared secrets cheap

The following is lifted from:
http://hanson.berkeley.edu/workinprogress.html and
http://hanson.berkeley.edu/cheapsecrets.ps

A simple mechanism is presented to allow one to buy a
verifiable secret known by more than one person. In the
unique sequential equilibrium, the secret can be bought
for an arbitrarily small sum, even if the secret getting
out would hurt each holder by an arbitrarily high amount.

Imagine two people share a secret which would hurt
them each $1000 worth if it got out. You offer to pay them each
$1 to (verifiably) tell you their secret. If this is a one-shot simultaneous
game, there are two pure-strategy equilibria: one where they both tell
and another where neither of them tell. But since the no-tell
equilibria makes them both better off, your chances aren't good.

What if, instead, you commit to paying only the first person who
tells you, and to paying more the longer you have to wait? You'll pay
$2000 a year from now, but you won't pay anything after that. Now
they both know they will each tell a year from now, if no one has told
before then. But then they each would tell you the day before, to be
first, for only
$1990. Following this reasoning back day by day, they would each
tell you the very first day, even if you only offered them $1!
Shared secrets can be bought very cheaply.

Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614
Received on Fri Feb 27 18:46:11 1998