Rishi Sunak, Ukraine and the Prisoner's Dilemma

One thing I don’t see often in the media, but hear a lot from friends across Whitehall and do at least see reflected in a lot of reporting, is how, on everything from climate change to the war in Ukraine Rishi Sunak’s policy instincts are fundamentally influenced by what might be considered his response to The Prisoner’s Dilemma.

The Prisoner’s Dilemma is a famous problem in Game Theory which has both a mathematical expression, and a narrative one. Let’s look at the narrative one first, with thanks to one of my preferred teaching aids for Game Theory.

Professor [Albert] Tucker’s Prisoners’ Dilemma Game is straight out of a Hollywood procedural crime drama where two prisoners are each offered a plea deal to rat on each other. The game illustrates the difficulty of acting together for common or mutual benefit given that people pursue self-interest.

Alan and Ben get caught for jointly stealing a car. The police suspect that they were also involved in a hit-and-run but do not have evidence to convict them on this charge. The two prisoners are interrogated in separate rooms. Alan and Ben each have two possible actions: to remain silent or to confess. Hence, there are four possible outcomes of the game:

Alan is silent and Ben is silent

Alan confesses and Ben is silent

Alan is silent and Ben confesses

Alan confesses and Ben confesses.

If Alan and Ben are both silent, then they each go to jail for one year for grand theft auto. If both prisoners confess, each goes to jail for 10 years. [But if only one confesses, he walks away with 0 jail time, while the other gets 15 years. They both know the details of this framework, and each knows the other also knows.]

(Pastine, Ivan; Pastine, Tuvana. Introducing Game Theory (Graphic Guides) (pp. 51-53). Icon Books. Kindle Edition.)

Expressed in a payoff matrix, it looks like this (don’t worry, you can skip this matrix entirely if it’s not your cup of tea):

Here’s the fun bit. Each of them must act simultaneously, without knowing what decision the other is making.

So, look at it from the point of view of Alan (while keeping in mind Ben’s point of view is identical). Alan can keep silent, or he can confess. Either way, his fate is partly in Ben’s hands. If Ben has confessed, then confession will get Alan 10 years rather than 15 for staying silent. If Ben has not confessed then confession will get Alan 0 years rather than 1 for staying silent.

So whatever Ben does, Alan is better off confessing. By confessing, Alan rules out the worst-case option of 15, and puts himself in the running for the best-case option of 0.

The problem with this, and the problem that this numerical model is designed to illustrate, is that taken collectively Alan and Ben would be better off both remaining silent, thus they get a combined two years, the lowest possible combined total. (The other possible combined totals being either 15 (15 + 0 or 0 + 15) years or 20 (10 + 10)). But individually they’re incentivized to confess.

Take it to another level – each of them knows the structure of the bargain, each knows that the other is being offered the same, and each therefore knows that the other is incentivized to confess. So if Alan assumes Ben will act rationally and confess, his only options are 15 years for staying silent, or 1 year for confessing. Alan will therefore act rationally and go for 1 year rather than 15.

This is a mathematical articulation of a kind of problem that comes up a lot in life. Sometimes it’s constructed deliberately (as in the kinds of plea bargains offered to suspected criminals in some legal systems), other times it simply occurs naturally. It doesn’t necessarily have anything to do with crime, and the actions aren’t necessarily confessing guilt versus remaining silent. All kinds of every-day activities can be covered by this model, as long as the benefits of co-operative are collectively the best outcome, but the fear that the other party(s) might not co-operate leads each party to pursue self-interest, ultimately damaging their own outcome.

So how do you ‘solve’ the Prisoner’s Dilemma? The only way is to change the incentives. In practical terms this is for some authority outside the articulated context of the dilemma to impose additional sanctions for ‘confessing’ and/or additional rewards for ‘remaining silent’.

Picture, if you want to continue the original narrative metaphor, Don Vito Corleone, the Godfather himself, assuring you that if you stay silent your family will be taken care of (in the good way) and there’ll be a nice bundle of cash waiting for you on release. On the other hand, if you confess . . . well, *shakes head sadly*.

This is why the solution to so many ‘public good dilemmas’ (of which the Prisoner’s Dilemma is an example) come from effective government. A body that has both the credibility, and the recourse to effective sanction, to compel co-operation for the collective good.

There are other solutions as well, but most of them revolve around the participants not being hyper-rational utility maximisers and having, say, a firm belief that their partner-in-crime will not rat on them no matter what, and therefore preferring to remain silent out of a sense of (for example) honour. (The possibility of remaining silent in order to maximise utility from a future relationship with your partner-in-crime, or with other persons who might not work with you if you’re known to be a rat, is a blog post for another day, and involves my favourite Game Theory exercise, The Ultimatum Game. Ultimately though it still fits in with the ‘rationalist’ solution as it results in the overall incentives being changed).

Being PM involves a lot of game theory (whether consciously or not) and the Prisoner’s Dilemma is going to crop up a lot because under our current system of international relations there is rarely an effective power above the level of national leaders who can sanction them. Therefore, when a PM finds themselves the participant in a Prisoner’s Dilemma, they’re usually playing it in its raw form.

Why does this matter for Rishi Sunak? Well, to be honest I have no idea if he’s even heard of the Prisoner’s Dilemma, but as an Oxford PPE, investment banker and later hedge fund manager, I would assume so.

What I am confident of, is that this way of thinking informs his policy preferences. This surfaced clearly when, as chancellor in the early period of the current war in Ukraine, a close ally of his said, “He thinks Putin will still be there and that there will have to be a deal with him and if that’s the case is it really worth the pain to the economy,”.

(https://www.thetimes.co.uk/article/sunak-ponders-political-future-as-wife-escapes-downing-street-goldfish-bowl-5gftqcmkk)

If Bob is going to confess anyway, what’s the point in risking 15 years, when we can accept that situation and get ourselves down to a solid 10 years?

In a way, it’s not an altogether inappropriate strategy. I use it myself a lot, especially where I need a mental short-cut to make a quick decision.

But, as the current status of the war in Ukraine suggests, in real life the payoffs aren’t always as fixed as they are in the PD matrix. How low would Russia’s probability of victory at the point have to have been in order for Sunak to change his calculations? After all, Ukraine was already a heavily damaged country, weaker economically than Russia. Peace, not victory, brings economic strength, and Russia’s peace is still far less disrupted than Ukraine’s. Win or lose, Russia is likely to remain the more relevant economic force. And ten years in prison (either literally in the original narrative, or metaphorically in the case of Ukraine) is still a lot. If you’re dealing with certainties it might be palatable. If you’re dealing with ever-evolving probabilities that you can yourself influence, probably less so.

From what I’m given to understand, he takes the same approach to climate change. A certain amount of warming is inevitable, so why waste economic strength fighting it, when we can preserve that economic strength to deal with it when it happens.

This approach – a lot of bad stuff is inevitable, so let’s not drag the strong who *might* be able to cope with it down with the weak who definitely can’t – shows through a lot of his private and semi-public positioning prior to his becoming PM as well.

I’m not psychic – I can’t see what’s in his head. And I’ve never discussed this with him. But I’ve built my career on being able to deduce how politicians see the world based on what is observable about them (and that skill – inferring the nature of what is invisible from what can be seen - is of course the true lesson of the ‘judgement of Solomon’), and I’m fairly confident on this one. Time will tell. I hope I’m wrong.