On the Rationality of Autocrats
Tyler Cowen has a nice piece on Vladimir Putin’s rationality and the related difficulty to deter him. It is quite often said or thought that autocrats like Putin are ‘mad’, or at least not rational in such a way that we can reliably expect that they will act as a reasonable person should. As it is often the case with statements about the ‘rationality’ or the ‘reasonability’ of someone, this is ambiguous. So let’s try to see what it could mean.
A good place to start is with a simple deterrence game-theoretic model. The player in red is some autocrat who is suspected to be ‘mad’, the player in blue is a group of nations (or an international organization like the UN or NATO) that is searching for deterring the autocrat to engage in some aggressive behavior toward some other country.
This is a sequential game with perfect information. The players are thought to be sequentially rational in the following sense:
- They order outcomes (i.e., the final nodes) from the most preferred to the less preferred.
- Their strategy choice does not contain an action (i.e., a choice at a particular node) that is not optimal given their preferences and their expectations of what the other player will do at the subsequent nodes.
Moreover, we suppose that both the structure of the game (including the player’s preferences) and their rationality is common knowledge, i.e., each knows both the structure and that everyone is rational, each knows this, each knows that each knows this, and so on.
With these assumptions, the solution of the game – the subgame perfect equilibrium – can be easily found by working backward. In this game, the subgame perfect strategy of the autocrat is [Status quo; Do nothing; Do nothing] and the one of NATO is [Respond; Strike back; Strike back].[1] At the subgame perfect equilibrium, the autocrat prefers to choose the status quo and the game ends. The point is that threatening is not credible because it is common knowledge that if the autocrat threatens and executes his threats, NATO will respond, which will be detrimental for the autocrat. Given this, it is common knowledge that the autocrat will never execute his threat and so there is no point threatening in the first place.
Suppose that, in contradiction with this conclusion, the autocrat threatens. What should we infer from this? How should the other player react? A possible answer is to assume that the autocrat’s threat is a random mistake that happens with a very low probability. In this case, the other player should not change his reasoning and play his subgame perfect strategy in the game starting at node 2:1. It is then expected that the autocrat will never execute the threat and so there is no need to respond to it. But what if we suppose that such “trembling hand mistakes” can’t happen? Then, the fact that the autocrat chose to threaten means that at least one of the above assumptions is false. It is obviously tempting to assert that the autocrat is not sequentially rational, in particular that he is prone to make noncredible threats. That would not mean that he would be willing to execute such threats if he has the opportunity to. In this case, the best response is to still disregard the threat. But it could also be that the autocrat does not always choose his best strategy, and so he is indeed susceptible to executing threats that will lead to a suboptimal outcome for him. This is most often what is implied by the claim that autocrats are ‘irrational’. Ironically, the putative irrationality of the autocrat makes his threats credible in some weird sense.
But wait. This last reasoning is probably accessible to the autocrat himself. It may be advantageous to threaten just to look irrational and to obtain some concessions from the other player who fears that the autocrat will engage in a costly war otherwise. For this to work, we should give up not the assumption that the players are rational, but that the structure of the game and/or the rationality of the players are common knowledge. As Cowen suggests in his article, autocrats are attracted by power. Power is a particular good, as it is essentially relational (I have power over someone else) and positional (to have power is to have more power than others). While even autocrats may be thought to be willing to tradeoff power against other goods, its peculiarities mean that they may be willing to engage in very costly behavior just to increase or preserve their power. The extent of the sacrifice autocrats are willing to do to preserve their power, especially within their country, is nonetheless difficult to evaluate.
What makes deterrence complicated in interactions with autocrats is that it is impossible to know their preferences because they are so dependent on their commitment to power. Autocrats are not irrational – they probably have well-ordered preferences and most of the time will reason sequentially. But their preferences are ambiguous and even weird from a certain standpoint. Smart autocrats know this and know they can take advantage of what others perceive as a relatively unpredictable behavior.
[1] Note that subgame perfect strategies define actions at nodes that can’t be reached at the equilibrium. This is crucial as it accounts for why a player will not engage in some action at a node because he knows that the other player will respond in a way that leads to a suboptimal outcome for him.