Category Archives: Uncategorized

Game theory and the Brexit crisis

Here is a very short, fairly non-technical description of the Brexit crisis seen through the game theory lens.

I start with some assumptions about the strategic payoffs (not in standard form for those acquainted with game theory) of the EU-UK Brexit negotiations. The payoffs tells us the net benefit from the possible strategic outcomes of the Brexit negotiations. Here we assume four strategic outcomes based on two decisions from two parties: offer a compromise
Brexit deal or do not offer a compromise Brexit deal. I use ‘UK’ to stand in for the United Kingdom, and ‘EU’ to stand in for the European Union. The smaller the number (in brackets), the lower (and worse) the payoff (e.g., -10 is worse than -7). Here is a payoff table:

  1. No compromises (no-deal Brexit): -10 (UK), -10 (EU)
  2. Deal with UK compromising: -8 (UK), -5 (EU)
  3. Deal with EU compromising: -5 (UK), -8 (EU)
  4. Deal with both parties compromising: -7 (UK), -7 (EU)

The exact numbers don’t matter for these purposes, simply their relative sizes. What this payoff table says is that a no-deal Brexit is the worst situation for both parties (both get -10). It’s hard to know if this is true in the real world, but it does not seem unreasonable. It also tells us that we have two ‘pure strategy’ Nash equilibria: #2 (UK compromise, No EU compromise) and #3 (No UK compromise, EU compromise). These are equilibria because if forced into one of these two situations, neither party would be better off opting out. For example, say the US forced the #3 deal somehow (the UK does not compromise, but the EU does). Once that agreement is in place, the UK is not better off by switching its position from no-deal to deal, since switching would result in a worse payoff of -7 (#4). Similarly, the UK does not benefit from switching from deal to no-deal, since that would result in a worse payoff of -10 (#1).

Unfortunately, there is no easy way to ‘force’ a deal, so get a standoff; both parties seem to be waiting for the other to compromise. We also have a deadline; if a deal is not made before October 31, 2019 , then #1 happens by default. Both parties know that a no-deal Brexit is the worst-case scenario, but do not seem compelled to give an inch. This is not a surprise for game theorists because unlike #2 and 3, #1 and #4 are not the same kind of equilibria. If both parties were somehow nudged into a #4 deal, for example, they both have an incentive to defect to another option that has a higher payoff where they do not compromise but the other side does. In this standoff, #1 may not be a choice, or optimal in any sense, but could still happen if a deal isn’t struck by the deadline.

Does Boris Johnson have a way out?

Boris Johnson, the current British PM has been a belligerent on the question of Brexit, and has made a number of decisions that signal preparation for a no-deal Brexit–promising money to help mitigate the financial consequences, and shutting down debate in Parliament. To many, this may seem like insanity (particularly if the no-deal Brexit really is the worse case scenario), but it could also be a clever strategy.

Boris Johnson and some kid

Once elected as PM, Johnson may have reasoned that if he can create a ‘credible threat’ of a no-deal Brexit, he will force the UK to compromise and solve the deadlock. He can create this credible threat by seeming to proactively remove #2 and #4 from the list of negotiating options (leaving only #1 and #3). He did this by reducing opposition debate in the House of Commons through parliamentary prorogation. This was a rare parliamentary maneuver (though not unfamiliar to Canadians), that could have been intended to signal that a compromise deal (that would require Parliamentary discussion) is now impossible. Once a British compromise deal is removed as a possibility, then the EU would have no choice but to compromise themselves, leading to agreement #3. This is because if the UK doesn’t compromise, the EU would be worse off with a no-deal Brexit (-10) (#1).

So Johnson’s quick work to prorogue Parliament may have been a tactic to convince the EU that the UK was creating a situation where no-deal was inevitable, thereby forcing their hand…

Another layer in the game…

However, now with the recent no-confidence vote in British Parliament, the threat of no UK compromise suddenly seems less credible. The British Parliament has changed its signal, effectively saying that they do not want a no-deal Brexit (or, for many, that they don’t want Brexit at all, and are trying to force conditions that will roll back the plan altogether).

In response to this, Johnson is pushing for an election. Why might he be doing this? Well, it is possible that the EU might also see an election as a credible threat of no compromise, particularly if it looks like Johnson might win with more support than his government currently has. Once an election is underway, there will be no government to negotiate with the EU, and less time to come up with a compromise deal acceptable to the UK parliament. It’s risky for Johnson–his government could easily lose an election. Nevertheless, if the election creates the credible threat of no-deal Brexit, he might again provoke some EU concessions.

It’s hard to know definitively what is going to happen in the short or long term. It’s also possible that there is no actual strategic intent here–maybe Johnson is just bluffing his way through this without much thought. What is clear, however, is that game theory gives us some language for understanding possible ways to think about the problem, and perhaps anticipate how the future will unfold…

Uncertainty, coordination and climate change

Today I spent a couple hours reading two papers authored by Scott Barrett, an environmental economist. One paper is “Climate treaties and approaching catastrophes” and the other (co-authored with Astrid Dannenberg) is “Sensitivity of collective action to uncertainty about climate tipping points”. The first paper is purely theoretical, and the latter has theory and an economic experiment.

Barrett’s focus in these papers is on climate change treaties. Climate change treaties are a challenge because costs of CO2 pollution are externalized, but countries are inclined to ‘free ride’ since there is no global government to punish non-signatories, or countries that fail to meet their commitments. For this reason, many argue that global-scale climate treaties are doomed to fail.

These papers show that coordination can work to address this climate treaty problem. Coordination occurs when actors work in their self-interest towards a goal that is collectively beneficial. When coordination is possible, there is no need for an enforcement mechanism; the treaties work because adhering to commitments are in the private interests of actors.

A number of conditions must exist to see effective coordination in abating climate change, but the one of Barrett’s focus is the reduction of uncertainty at the threshold which a climate catastrophe would occur. In short, as uncertainty in the threshold gets smaller, the more likely that an actor will follow through with abatement measures–like reducing CO2 emissions. Provided the uncertainty is small enough (in proportion to the damages resulting from climate change, and inversely proportional to the difference between costly abatement and the benefits of climate change) then actors will choose to take measures to avoid catastrophe.

Lucky for you, I wrote some R code that you can use to experiment with the model he proposes!

In addition to demonstrating this theoretically, Barret and his co-author use some hypothetical choice experiments to test this theory in the lab. The experimental results are fairly consistent with their theoretical findings; the authors found that most people would choose to abate when the catastrophic tipping point is certain, and nobody would abate when it is very uncertain.

What this research shows is the importance of reducing scientific uncertainty, and specifically, that reducing uncertainty about thresholds of climate catastrophes may be key to getting useful and effective climate treaties.

Data, infant mortality and anti-abortion activism

The following question crossed my mind recently: how many lives are lost from excess infant mortality?

I asked this question because I wondered if anti-abortion activists couldn’t better spend their time saving the lives of children that died in their first year of life, rather than protesting at abortion clinics. Saving the life of a child who has been born seems like an easier political task, and will almost certainly be more effective.

We have a pretty good sense that this is theoretically possible because of the considerable variation in infant mortality that exists worldwide. Most poor countries have high infant mortality rates (IMR), and most rich countries have low infant mortality rates. There are a number of countries in Africa with IMR above 50 per 1000 live births (meaning 50 children die in their first year for every 1000 live births). There are rich countries with IMR below 5. The difference between these numbers–roughly 45 per 1000 births–tells us that preventing infant death could be very impactful.

In the US, there is variation in IMR across ethnic communities. The IMR among African Americans is 11.4, and 4.9 among whites. All of these babies are being born in the US, but white babies are much more likely to survive past 1 year of age. Preventing infant deaths in African American and other marginalised communities would save lives without the controversy.

In Canada, the IMR for the Inuit population is a shocking 17.7, three times the national average. Improvements to maternal care and access to quality health care in remote rural areas would save the lives of many living infants. Given that there is little popular or political appetite for outlawing abortion in Canada, reducing IMR among the Inuit seems infinitely more productive way to spend time for people who are concerned with preserving lives of children.

Globally, the potential numbers of lives saved would be much greater. I used World Bank data to estimate the number of infant lives that could be saved worldwide if we lowered IMR to 5 per 1000 for in every country in the world that currently has an IMR greater than 5. You can download the R code here. According to these calculations, we could save around 3.6 million children every year by lowering IMR to 5.

3.6 million children every year!

Practical solutions for lowering infant deaths in poor countries are fairly well known. Worldwide, many infant deaths occur because of preventable infection. Most of these infections could probably be treated with investments in medical infrastructure and better access to antibiotics. Other deaths are caused by an absence of simple medical interventions and lack of training. It seems that anti-abortion activists could put their time into lobbying pharmaceutical companies to increase affordable access to antibiotics in developing countries, or improving access to maternal care in the developing world.

Closer to home, we could do more to increase access to health care and support mothers living in poverty, particularly in rural and remote areas. There are many lives to save, and best of all, none of them come with legal wrangling or political and social controversy. It seems that anyone who genuinely cares about saving lives for their own sake could do a lot about it without entering the quagmire of anti-abortion activism.