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Assuming two agents A and B, where Agent_A is the blackmailer, blackmail has the following properties:

Agent_A offers to omit acting in a way that is undesirable according to Agent_B for the purpose of controlling the actions of Agent_B in such a way that is desirable according to Agent_A.

Consider a situation where Agent_A creates a desirable product that Agent_B wants. Such a case does not satisfy all of the above conditions since Agent_A offers Agent_B to act in such a way as to achieve a world state that has a higher ranking according to Agent_B than the current world state, namely the action of acquiring the product created by Agent_A.

The important difference between blackmail and trade scenarios that are not considered blackmail is that blackmail scenarios offer the agent that is being blackmailed the possibility to be worse off whereas a trade scenario offers the agent the possibility to achieve a world state that is ranked higher according to its utility-function.

A trade is considered to be blackmail when it benefits one party involved in a trade by offering to omit an action that would make all other parties worse off. More specifically, if an offer to omit an action that harms other parties was made for the benefit of the party making the offer then the action is considered to be blackmail.

The properties of blackmail are thus defined to be:

(1) The omission of an action is offered by one party.
(2) The action would make all other parties involved worse off.
(3) The purpose of offering to omit the action is to control the actions of all other parties in such a way as to make the party offering to omit it better off.