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. ============ 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. ============ 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.