The Intimidation Game

If you want to control someone, all you have to do is to make them feel afraid. ― Paulo Coelho

Many people (too many) are familiar with the experience of being bullied, intimidated, or threatened (Juvonen & Gross, 2005). Fewer people have themselves bullied, intimidated, or threatened others. This differential may reflect different incentives. When multiple aggressors converge on one victim, there is little to be gained for the individual aggressor. The probability of victory is high but the value of the spoils is low. Yet, mobbing occurs (Keashly, 2019). By contrast, the individual aggressor who attacks many others (not all at once), may hope to succeed sometime and with someone. This broadcasting strategy can be observed on the internet where more people have been exposed to threats and scams than have engaged in such.

Among humans and other animals, the threat of aggression is more common than actual, physical, aggression. Physical aggression is risky. It can lead to injury or death. Even when fighting erupts, it is often limited to ritualistic displays, bluster, or saber-rattling (Carlson et al., 2018; De Boer & Kohlhaas, 2017). Threatening behavior has not disappeared from our behavioral repertoire because it sometimes works. A bluff is rewarded if it is perceived as credible. Then the aggressor gets something for (almost) nothing (Li et al., 2016).

Neither aggression nor docility is a dominating strategy. Both strategies present themselves in an uncertain environment, where each agent tries to figure out how likely it is that the other will yield or retaliate (Grüning & Krueger, 2021). To make this sort of prediction, an agent first needs to know their own preferences and the preferences of the other. As a first stab at what an intimidation game might look like, consider the extensive-form presentation in the figure below. P1 is the potential intimidator or atttacker; P2 is the responder or defender. The numbers refer to preference ranks, where larger numbers are better. The numbers to the right of the comma show the aggressor's preferences.

J. Krueger

The game begins with a status quo, which is rather pleasant (i.e., Pareto-efficient) overall, with the sum of the preference ranks being higher than it is in any other outcome scenario. There is, however, an inequality in that P1, the attacker, only realizes their second-best outcome. P1 has an incentive to move to the right and threaten P2, hoping that P2 will then move to the left and cede the best outcome to P1. In this scenario, however, P2 would end up with the worst outcome; so why should they fold? Alternatively, P2 moves right and pushes back. Now it is P1’s turn to choose between resigning, which would yield the worst outcome, and fighting, which delivers a poor outcome to both parties.

How should players in this game behave and how might they go wrong? A rational game theorist would note that P1 should refrain from intimidation. Knowing their own and P2’s preferences, and using backward induction, P1 could foresee that intimidation will lead to pushback and ultimately to mutual attack. A myopic (or prideful) P1, however, will only see the beckoning best outcome, to be obtained after successful intimidation. P1 would note that their 4 > 3, and ignore the fact that for P2, 1 < 3 or 2.

The game would be radically different if P2 preferred caving to threat (2) to mutual fighting (1). In this revised game, P1 has an incentive to intimidate, but only if they predict that P2 is not myopic. A myopic P2 would push back against intimidation, only to then end up as the loser in an actual fight. In this version of the game, intimidation is not a bluff. This alternative version is — or should be — unlikely, however, because P2 agents who are known to cave to intimidation will be exploited repeatedly until they disappear from the scene. Evolution favors individuals who prefer a good fight to instinctively yielding to threat. The P1 intimidator should know this.

The intimidation game we have explored here is an extension of the power game (Krueger et al., 2022) and attack-defense games (Sheremeta, 2019). Here, we ask what will happen if an inequality-averse agent, P1, decides to rebel. No matter which version of the game we consider, we can note that all joint outcomes are worse than the status quo. There is an interesting moral implication: What is the value of equality relative to the value of collective prosperity? The intimidator might say that they are motivated by equality, but we see they would be even happier if their intimidation were successful. Thus a profession of equality preference would be of dubious credibility. Moreover, P1's expressed dissatisfaction with the status quo can not only be framed as inequality aversion, which sounds morally good, but also as jealousy, which sounds morally bad.

Interpersonal games involving conflict, uncertainty about others’ preferences, and a limited ability to simulate the future, are recurring challenges in everyday life. It is tempting to advise everyone to keep the peace when some can imagine themselves doing better if they rebelled. When the value of rebellion is celebrated (Kashdan, 2022; reviewed by Krueger, in press), the emphasis tends to be on the removal of gross injustices (e.g., oppression), and the rebel’s self-interest or intent to intimidate is easily overlooked. The potential costs of intimidation are borne by all parties and they can be considerable; and they have a way of sneaking up on the myopic mind.

Note. After this essay was published, I learned that there is a book (Strassel, 2017) with the same title. This sameness was unintented on my part. The book, as it turns out, seems rather interesting as it discusses threats to free speech as they arise from progressive circles in your society. Intimidation, it seems to me (see the figure as well), is something worth rebelling against.