The Atlantic's Megan McArdle explains how economics can save you if you find yourself kidnapped by pirates. The number one suggestion: keep your mouth shut.
According to a hostage negotiator quoted by This American Life, giving away this information is apparently typical of hostages and is counter-productive to their release as it narrows the bid-ask spread. Economists would describe hostage negotiation as a bilateral monopoly price negotiation that is structurally just a special case of chicken. That is, unlike a barrel of oil or a freight car full of soybeans which can trade on an extremely liquid market with innumerable buyers and sellers, a hostage has exactly one seller (the kidnappers) and exactly one buyer (the employer and/or family of the hostage). When there is only one buyer, the opportunity cost for ransoming the hostage is zero. Likewise, the employer and/or family has no realistic alternative means to recover the hostage. In order for everybody to walk away happy, we need a cooperate-cooperate outcome: the kidnapper has to give up the hostage and the employer/family has to give up a ransom. This structure also characterizes art theft, which in practice is not a matter of fencing art on the black market but ransoming art to a museum's insurance company.