The Specker Derivative Game has several variants.
This does not work. Price has no meaning.
SDG/decision:
Start with any decision problem pnp in NP.
NP is the set of all problems for which there is an efficient certifier.
(See Kleinberg/Tardos, chapter 8)
Predicates partition instances of pnp.
Raw material: instance j in pnp. Certificate is secret.
Finished product: solution for j showing that j in NP.
Certification: seller shows certificate that j in pnp.
quality: 0 or 1. 1 only if solution for j shows that j in pnp.
derivative has a price p.
If buyer successfully finds a certificate that j is in pnp,
the buyer gets paid back 2*p by the seller.
If the buyer does not find a certificate, nothing is paid back.
So the risk of buying a derivative is that
you might lose all your money or you might double it.
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SDG/maximization:
Start with any maximization problem mnp whose decision
version is in NP. Given a certificate for achieving
a certain value, we can efficiently check whether it holds.
Predicates partition instances of pnp.
Raw material: instance j in mnp and a value q that the
seller can achieve through a secret certificate.
Finished product: solution for j with quality q'.
derivative has a price p.
if buyer successfully finds a solution of value p*q
or better than the seller claims,
the buyer gets paid 2*p by the seller.
If the buyer finds a lower quality solution, nothing is paid.
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SDG/classic:
This works in a less general context: MAX-CSP.
For comparison: let's use the same pay scheme for the classic version.
If the buyer successfully finds a solution that is above or
equal to the price p,
2*p is paid back by the seller.
Otherwise nothing is paid back.
When the seller puts a derivative d on the market at price p,
the claim is that s/he has a solution of quality p
for any raw material satisfying the predicate.