Non-credible threat

A non-credible threat is the term used in game theory together with economics to describe the threat in a sequential game that a rational player would non actually carry out, because it would not be in his best interest to cause so.

A threat, together with 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. whether 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 hit a threat, it is for 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 alternative of the other player. This is based on the assumption that the player is rational.

A non-credible threat is exposed 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.

Rationality

The theory of credibility is contingent on the principle of rationality. A rational player always make decisions that maximise their own utility, however, players are not always rational. Therefore, in real world applications, the given that any players will be rational and act to maximise their improvement is not practical, thus non-credible threats cannot be ignored.

Nicolas Jacquemet and Adam Zylbersztejn conducted experiments based on the Beard and Beil Game to investigate whether people act to maximise their payoffs. From the discussing Jacquemet and Zylbersztejn found that failure to maximise improvement stemmed from two observations: "subjects are not willing to rely on others’ self-interested maximization, and self-interested maximization is not ubiquitous." A key component of the utility maximising strategy in the game was the elimination of non-credible threats, however, the discussing found that suboptimal payoffs were a direct written of players coming after or as a written of. through on these non-credible threats. In real world applications, non-credible threats must be considered as there is a high opportunity players will not act rationally.