Nash Totalitarianism

In joyful commemoration of the delightful occasion of Fidel Castro’s death.

Around 1990 a friend of mine visited Cuba. At an outside café she conversed with a native, who told her that a security agent was tailing her and that after she walked away, the agent would approach the native and question him about their conversation. The native surreptitiously identified the agent. After the conversation was over and my friend had walked a few tens of yards away, she looked back. Sure enough, the person identified as a secret police operative had approached the native and was questioning him.

It seems clear that the citizens of such a country oppose the state because the state does things like this, and the state does things like this because the citizens oppose the state. That is, totalitarian regimes are, at least in part, self-fulfilling prophecies: The State censors information, is suspicious of those who have contact with foreigners, and jails advocates of liberalization because it knows the people hate the State. And the people hate the State because it censors information, is suspicious of those who have contact with foreigners, and jails advocates of liberalization.

This particular self-fulfilling prophecy is an example of an important concept in game theory, Nash Equilibrium.

A Model

Consider a state with two possible moves: totalitarianism, T, and democracy, D. (By “state” I mean the permanent fixtures of the government—the Department of Education, the Intelligence Service, etc.—not necessarily a particular political party.) The state would rather persist than be dissolved.

Suppose the polity has two moves: oppose the continued existence of the state, O, and acquiesce in the state’s continued existence, A. Naturally, we assume the polity would rather have democracy than totalitarianism.

Also assume the state will definitely survive if the polity acquiesces, whether the state is playing T or D. If the polity opposes the state, the probability of the state being destroyed is positive but less than one if the state plays T, and is one if the state plays D.

Finally, suppose (optimistically) that both players prefer democracy to totalitarianism, ceteris paribus, and that opposition requires effort and risk, so the polity would prefer acquiescence to opposition if it didn’t care about the nature of the state. The payoff matrix is

State’s moves on rows; polity’s moves on columns
Acquiesce Oppose
Totalitarianism Polity: 0
State: 7
Polity: 5
State: 5
Democracy Polity: 10
State: 10
Polity: 6
State: 0

This payoff matrix captures the features mentioned in the previous paragraphs. To see this…

First put your hand over the Oppose column. Looking at the Acquiesce column, i.e., the polity acquiescing to the state’s existence, we see that the state would rather have democracy than totalitarianism. (Since the state’s payoff with Democracy, 10, is greater than its payoff with Totalitarianism, 7.) This embodies the hopefully-not-too-optimistic assumption that if the population is cool with it, the state would rather exist with democracy than totalitarianism. (If the state is indifferent, or would rather have totalitarianism, then the problem is even worse than this payoff matrix depicts.)

Next, put your hand over the A column. Looking at the O column, that is, the situation in which the polity opposes the state, we see that the state would rather have totalitarianism than democracy (since 5 is greater than 0). That is to say, the state wants to stay in power, so given that the populace opposes it, it will choose to do things like implement censorship, follow people around and monitor their contact with foreigners, etc.

Next, put your hand over the D row. Looking at the T row, that is, the situation in which the state is totalitarian, we see the polity would rather oppose the state than acquiesce in its continued existence. (Since the polity’s payoff with Oppose, 5, is greater than its payoff with Acquiesce, 0.) That is, people dislike totalitarianism.

Finally, put your hand over the T row. Looking at the D row, that is, the situation in which the state is democratic, we see the polity would rather acquiesce in the state’s continued existence than oppose it. (Note 10 is greater than 6.) That is, people like democracy.


There are two Nash equilibria: (T, O) and (D, A). This is because…

(1) Given that the state is totalitarian, the polity’s best response is to oppose it. And given that the polity opposes it, the state’s best response is to be totalitarian.
(2) On the other hand, given that the state is democratic, the polity’s best response is to acquiesce in its continued existence. And given that the polity acquiesces in its continued existence, the state’s best response is to be democratic.

The democratic equilibrium is unanimously preferred to the other one, i.e., both players get a payoff of 10 in the (D, A) equilibrium, and a payoff of only 5 in the (T, O) equilibrium.

If both players agree that the (D, A) equilibrium is better, what’s the problem?

Yeah, about that…

Getting Yanked Toward Nash Totalitarianism

One of the implicit assumptions above is that the political situation is not hit by random shocks that might perturb it. But everything in life is actually hit by random shocks. A big shock might be a war, which necessitates (or at least could be argued to necessitate) more controls on speech, etc. (“War is the health of the state.”) This could bounce us into a totalitarian situation, which quickly ossifies into an equilibrium – the bad equilibrium. See, e.g., Russia circa World War I.

Why doesn’t the state simply announce its intention to democratize and then do so? Such an announcement would be credible, since (D, A) is a unanimously-preferred Nash equilibrium. Right?

One reason this might not be possible is that the state may be subject to random shocks to its preferences, such that it occasionally has temporary episodes of stronger preferences for democracy—e.g., liberalization periods a la Gorbachev—which the polity knows are temporary. For this reason if the state democratizes the polity may quickly vote it out to ensure it doesn’t revert to T a short while later. Such a possible reversion is not captured in the above game because that game has nothing about a preference for T, in fact it assumes a preference for D.

When we think of totalitarian regimes in the real world, though, we think of them initially becoming totalitarian for some reason, some reason outside the above game (i.e., a reason other than that it happens to be a Nash equilibrium). For example, a state implements suboptimal economic policies that induce emigration (bluntly, everyone’s starving to death; they’re desperate to get the fuck out of Dodge). In order to staunch the emigration the state imposes border controls, this makes the people hate the state, so they oppose it and the state finds it necessary to censor information, jail dissidents, etc.

Thus a larger, more accurate game would have the state making a joint choice, choosing its political nature from {D,T}, while choosing other policies, e.g., economic ones, subject to constraints on the joint choice, e.g., blatantly suboptimal economic policies are not tenable with democratic political policies. Given this, the problem is that the state has announced its intention to choose D but also its intention to maintain suboptimal economic policies; the polity knows this is not tenable in the long run and that the state will eventually find it necessary to revert to T. So the polity optimally chooses to take advantage of the liberalization to eject the state while they can. Of course, the state knows this will happen,(*) so it won’t take a chance on liberalization.

The shocks affecting the state could be shocks to preferences (i.e., a larger preference for democracy) or beliefs, (i.e., true believers who believe the state’s desired policies are compatible with democracy and that the polity also believes it). E.g., Mikhail Gorbachev believed socialism would work, given a bit of openness, so he thought Marxist economics + D was a possible choice. He found out differently.

It may also be that the state cannot in fact credibly commit to choosing democracy. For example, the head of state—the Gorbachev—may actually prefer democracy, while the nomenklatura below the head of state are opposed to it, e.g., because they’ll lose their jobs (think of employees of the secret police agency or the censoring bodies, etc.) This is not captured in the payoff matrix above because it models the state as a unitary actor. If that is relevant then the state cannot in fact credibly communicate a preference for democracy. In fact, the state has a direct preference for T. In that case the Nash explanation of T is unnecessary—the explanation would shift more to a path-dependency explanation: once I’ve got my job in the Ministry of Censorship I want the T regime to persist, since my job is terminated if the regime is dissolved.

None of this suggests that totalitarianism is inevitable. It certainly suggests we always have to be on our guard, and that in setting up institutions, we must make it THE priority to keep government’s power limited.

* To be motivated to avoid liberalization, the state need not believe that its desired economic policies are long-run incompatible with democracy. It need only believe that the polity believes that.


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