In this game we imagine that Ebenezer Balfour (the captor) has arranged for the kidnap of his nephew David Balfour in order to keep David (the captive) from his rightful inheritance.
In one version of the story things look bleak for David. He knows the identity of his kidnapper. Should he escape then he will regain his inheritance and his captor will go to jail. To prevent this the captor has only one possible course of action; to send David into exile on an island from which he cannot escape and where he will die an untimely death.
While this may be a solution to an extensive form game, and is therefore a Nash equilibrium, it is not a desirable outcome to the game from David's perspective.
David tells his captor that if Ebenezer lets him go then he will not turn Ebenezer over to the authorities, and Ebenezer can keep the inheritance. Is this a credible commitment? Is there anything Ebenezer can do to make David stick to his commitment? The answer to both questions is no, and so the commitment is not made.
But does that need to be the end of the story? Not necessarily. Suppose David has a skeleton in his own closet; a dastardly deed that would send him to prison were it to be discovered by the authorities. Now David has something to offer in order to make his commitment credible. He can reveal his darkest secret to Ebenezer in exchange for his release. Now Ebenezer knows that David will abide by the agreement not to reveal the name of his captor, since the captor now has it in his power to send David to prison if David rats him out.
Click here to download a self-extracting zip file with the original story. The file is about 200Kb, so be patient. Once you have downloaded it you need only click on the file named kidnapped.exe.
Robert Louis Stevenson