Threat (game theory)

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A threat is the credible announcement of an unpleasant measure against someone in order to influence his future course of action in such a way that an advantage can be gained from it.

Background and environment

Based on the consideration of parlor games , the term is used in game theory (as a discipline of mathematical economic theory) to investigate strategies for individual actors in a game-theoretical problem.

Within the sequential games, the action of the threat represents a conditional strategic move. In order to achieve a subjectively meaningful game result, one's own reaction to the previous action of the others is determined before this. Determining your own approach is called an answer rule .

This restriction of one's own decision-making scope to a predefined rule places conditions on the action of the opponent and thus on the further course of the game. Hence the classification of the threat as an action within the contingent strategic trains.

The definition of a reaction pattern initially represents a limitation of its own, which will develop to one's own advantage due to its effect within the sequence of actions.

The counterpart to the threat is the promise . In contrast to the threat, the aim here is to influence the action of the game partner by means of positive effects.

Game theory effect

If a player does not have the advantage of the first move, he can still secure a strategic advantage by committing to certain follow-up actions by trying to influence the opponent on his first move. For this purpose, a condition is formulated, the fulfillment of which is to have a negative impact - the threat. Due to this condition and its associated consequences, the variety of decision options is reduced in such a way that the remaining options allow your own advantage. The use of a threat only makes sense if the opponent is supposed to choose the alternative course of action that he would probably not have chosen without the threat. Otherwise the threat is unnecessary and only serves as additional security. From a diplomatic point of view, the promise is very likely the more appropriate means. It is crucial that the opponent assumes that the negative impact will also be enforced. If he has serious doubts about the credibility of the threatening person, the threat loses its influence accordingly.

Premises

In order for a threat to be effective, it is necessary that it meets the following requirements: Effectiveness and suitability must be given. The content of the threat must have a negative impact on the person threatened. For example, if you threaten a chronic truant with expulsion from class, you will hardly achieve constructive cooperation.

Credibility is necessary. The playing partner must be able to assume that the threat will be met in the event of non-cooperation. It must also be ensured that the opponent is aware of the threat.

Variants of the threat

The threat is first divided into compelling or deterrent threats according to the intended reaction or action of the opponent. There is also the destructive case of the empty threat.

Coercive threat

If the opponent is to preferentially carry out a certain action on the basis of the threat or if a specific alternative action is to be chosen, then it is a compelling threat.

Example: An example of the coercive threat might be asking a school child to do their homework. Otherwise a television ban will be enforced. The parents limit their own freedom of action (allowing or prohibiting television) to the refusal alternative. The condition for this is that the child is asked to do their homework, i.e. to choose a certain course of action from the various alternatives (playing, visiting friends, cycling, ...).

Dissuasive threat

If the playing partner, as opposed to forcing him, refrains from an alternative course of action, it is a deterrent threat.

The punishment of soldiers for disobeying orders is an example of the deterrent threats. The soldier is deterred with the punishment (negative effect) from deserting (condition). He is very likely to choose the alternative of obedience desired by the commander.

Empty threat

If an announced threat does not fulfill one of its premises, it becomes ineffective. The ineffective announcement of the negative impact will not have any effect on the opponent. One speaks of an empty threat . The threat therefore requires an effective negative impact and the credibility that it will be met if the condition is met.

For example, it is unsuitable to make a threat when one's own commitment is to pursue a self-dominated strategy. In this case, the effect of the self-commitment is associated with negative effects for the opponent and is therefore effective and probably also suitable, but the threat of self-damaging action makes the threat appear implausible.

literature

  • Pindyck, Rubinfeld: Microeconomics 6th Edition, Verlag - Pearson -Studium, Munich, 2005
  • Dixit, Nalebuff: Game theory for beginners Verlag - Schäffer-Poeschel, Stuttgart, 1997