Examples of Non-credible threats
Market Entry Game
An example of a non-credible threat is demonstrated by Shaorong Sun & Na Sun in their book Management Game Theory. The example game, the market entry game, describes a situation in which an existing firm, firm 2, has a strong hold on the market and a new firm, firm 1, is considering entering. If firm 1 doesn’t enter, the payoff is (4,10). However, if firm 1 does enter, firm 2 has the choice to either attack or not attack. If firm 2 attacks, the payoff is (3,3) whereas if firm 2 doesn’t attack, the payoff is (6,6). Given that firm 2’s optimum payoff is firm 1 not entering, it can issue a threat that they will attack if firm 1 enters, to discourage firm 1 from entering the market. However, this is a non-credible threat. If firm 1 does decide to enter the market, the action that is in the best interest for firm 2 is to not attack as this leads to a payoff of 6 for the firm, as opposed to the payoff of 3 from attacking.Eric van Damme's Extensive Form Game
Eric van Damme's Extensive Form Game demonstrates another example of a non-credible threat. In this game, player 1 has the choice of L or R, and if player 1 chooses R, then player 2 has the choice of ''l'' or ''r''. Player 2 can threaten choosing ''l'' with a payoff of (0,0) to entice player 1 to choose L with a payoff of (2,2), as this is the highest payoff for player 2. However, this is a non-credible threat as, if player 1 does decide to choose R, player 2 will choose ''r'' as their payoff is 1 as opposed to ''l'' which has a payoff of 0 for player 2. Given that action ''l'' is not in player 2’s best interest, their threat to play that is non-credible.Rationality
The notion 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 assumption that all players will be rational and act to maximise their utility is not practical, thus non-credible threats cannot be ignored.Experiment using the Beard and Beil Game (1994)
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 study Jacquemet and Zylbersztejn found that failure to maximise utility 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 study found that suboptimal payoffs were a direct result of players following through on these non-credible threats. In real world applications, non-credible threats must be considered as there is a high possibility players will not act rationally.Notes
See also
* Dynamic inconsistency *External links
* * Ellsberg, Daniel