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Source: Non-credible threat

A non-credible threat is a term used in game theory and economics to describe a threat in a sequential game that a rational player would not actually carry out, because it would not be in his best interest to do so.
A threat, and its counterpart – a commitment, are both defined by American economist and Nobel prize winner, T.C. Schelling, who stated that: "A announces that B's behaviour will lead to a response from A. If this response is a reward, then the announcement is a commitment; if this response is a penalty, then the announcement is a threat." While a player might make a threat, it is only deemed credible if it serves the best interest of the player. In other words, the player would be willing to carry through with the action that is being threatened regardless of the choice of the other player. This is based on the assumption that the player is rational.
A non-credible threat is made on the hope that it will be believed, and therefore the threatening undesirable action will not need to be carried out. For a threat to be credible within an equilibrium, whenever a node is reached where a threat should be fulfilled, it will be fulfilled. Those Nash equilibria that rely on non-credible threats can be eliminated through backward induction; the remaining equilibria are called subgame perfect Nash equilibria.