Threats

Figure 1 Extensive form game: Player 2's threat to defend is not credible

Notice that, in any case, threats occur when preferences are opposed in some way: if they are congruent—that is, k′Pi, jk—then the threat is redundant. The success of a threat by i in terms of determining j's actions depends upon the size (or seriousness) of and the relative utility for j of k and k′. Also, the actions of the threatened party, j, must be observable, directly or indirectly, and it must be believed (at least by j) that the threat will be carried out should j's actions require it. These issues concern whether or not a threat is credible. We can conflate these two cases by supposing that the implementation of imposes a (monitoring, psychological, monetary, or other) cost c on i and that ui(k-c) < ui(k′). In this case i's threat is not credible: if j does not choose as i would prefer, i will become worse off by carrying through on the threat and punishing j. For example, parents may not actually be willing to chastise a naughty child after it behaves badly (even though they could observe it perfectly) or a government may not be able to monitor illegal drugs use in private homes (even though it could punish without much psychic cost).

Analysts working with game theory have discussed these issues at some length. As an example of a noncredible threat, consider the extensive form game in Figure 1. Here Player 1 chooses attack or peace. Player 2 would like to play defend if 1 attacks, but this is not a credible threat: if Player 2 defends, then he or she is worse off (in terms of a payoff of /2) relative to capitulating (where he or she gets− 1).

Notice that if Player 2 could commit to the defend threat in some way—perhaps with an automatically deployed missile launch in response to an attack—he or she may be able to avoid an attack in the first place. The cold war strategy of mutually assured destruction, in which nuclear annihilation results from either side attacking, may be an example of such logic.

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