Nicolas Jacquemet and Adam Zylbersztejn conducted experiments based on the beard and axe game to determine if people are acting to maximize their payments. From the study, Jacquemet and Zylbersztejn found that the inability to maximize benefits is due to two observations: “Subjects are not willing to rely on the selfish maximization of others, and selfish maximization is not pervasive.”  A key element of the strategy to maximize value in the game was the elimination of non-credible threats, but the study found that suboptimal payments were the direct result of players implementing these non-credible threats.  In real-world applications, there is no need to consider credible threats, as there is a high probability that actors will not act rationally.  The concept of credibility depends on the principle of rationality. A rational player always makes decisions that maximize his own profit, but players are not always rational.  Therefore, in real-world applications, the assumption that all actors are rational and act to maximize their benefits is impractical, so non-credible threats cannot be ignored.  A non-credible threat is made in the hope that it will be believed, and therefore the imminent unwanted action does not have to be carried out.  For a threat to be credible in equilibrium, it is filled whenever a node is reached where a threat is to be encountered.  Nash equilibria based on non-credible threats can be eliminated by reverse induction; the remaining equilibria are called the perfect Nash equilibria of the subset.   Paragraph 2. For the purposes of this chapter, “credible threat of violence” means a statement or conduct knowingly and intentionally based on conduct that serves no legitimate purpose and that causes a reasonable person to fear for the safety of the person or for the safety of his or her immediate family.
A threat and its counterpart – an obligation – are both defined by american economist and Nobel laureate T.C. Schelling, who said: “A announces that B`s behavior will lead to a reaction of A. If this response is a reward, then the announcement is an obligation; If this reaction is a penalty, then the announcement is a threat.  Although a player may make a threat, it is only considered credible if it serves the best interests of the player.  In other words, the player would be ready to perform the action that is threatened regardless of the other player`s choice.  This is based on the assumption that the player is rational.  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 execute because it would not be in his interest to do so. Shaorong Sun & Na Sun shows an example of a non-credible threat in their book Management Game Theory. The example game, the market entry game, describes a situation in which an existing company, company 2, has a strong influence in the market and a new company, company 1, plans to enter. If company 1 does not occur, the payment is (4.10). However, when Company 1 occurs, Company 2 has the choice of attacking or not attacking. If company 2 attacks, the payment is (3.3), while if company 2 does not attack, the payment is (6.6).
Since the optimal payment for Company 2 is that Company 1 does not enter, it can threaten that it will attack if Company 1 enters to prevent Company 1 from entering the market. However, this is not a credible threat. If Company 1 decides to enter the market, the action that is in the best interest of Company 2 should not be attacked, as this will result in a payment of 6 for the company, as opposed to the payment of 3 from the attack.  Eric van Damme`s Extensive Form Game shows another example of a non-credible threat. In this game, player 1 has the choice between L or R, and if the player chooses 1 R, then player 2 has the choice between L or R. Player 2 can threaten a payment of (0.0) to deceive Player 1 by choosing L with a payment of (2.2) as this is the highest payout for Player 2. However, this is not a credible threat, because if player 1 decides to choose R, the player chooses 2 R because his payout is 1, unlike l, which has a payout of 0 for player 2. Since Action l is not in the best interest of Player 2, their threat to play is not credible.
 For the purposes of this chapter, the term “credible threat” means a threat made with the obvious intent and capacity to carry out the threat. A credible threat does not need to be expressed verbally. This game theory article is a stub. You can help Wikipedia by extending it.