Last year, I published a blog called, somewhat tongue in cheek, Team Based Learning solves Brexit This year, as the #brexit negotiations go the wire, I took the (last?) opportunity to use Brexit as a case study in #gametheory.

Caveat – I do not claim any special insights on Brexit, nor indeed Game Theory. This is blog is not intended to be political, or partisan. It’s chiefly about the application of #teambasedlearning in an online context. If that interests you, read on..

As #teambasedlearning aficionados will know, application exercises often take the form of ‘complex problem, simple output’. And what could be simpler than representing the outcome of the Brexit negotiations as a grid?

	European Union
UK	Make Concessions	Hold Firm
Make Concessions	A = Deal	C = Barnier Deal
Hold Firm	B = Boris deal	D = No deal

Of course, being able to tackle this problem requires some knowledge of game theory, which I had covered in the Readiness Assurance Protocol (see below). Knowledge of the Brexit context is useful – fortunately, most students in a UK University are well informed on this topic (quite possibly better informed than me!) and I left them a few links to some recent news & analysis as pre reading for the session.

Departing slightly from the normal #teambasedlearning practice of permanent teams, I randomised the teams in zoom breakout rooms. This is because:

1. the exercise is not linked to their group assessment (it is, however, strongly linked to their individual assessment –  applying game theory to a business scenario of their choosing – this provides a powerful motivation for students to engage in this activity).
2. With less than 100% attendance (about 85/125 showed – not unusual at this stage in semester) I could not guarantee that all teams would be at full strength
3. In the online context particularly, I find students really appreciate the variety of working with different people each week and thus introducing more of the social element into the sessions.

They had about 20 minutes to create a payoff matrix and derive their prediction, which we discussed in class for 20 minutes (a good rule of thumb – discussion time and exercise time should be about the same length). I took a zoom poll to find out that distribution of predictions.

So, what were the results? Well, before I reveal the outcomes, the important thing here is not the political implications of the results, but more that the exercise (as I hoped) revealed a whole number of game theoretic scenarios. Which are: 

A Prisoner’s Dilemma

Five of these, the most popular outcome : The Prisoner’s Dilemma is well described in game theory literature. In this scenario, although both sides want a deal (top left), the rational outcome is a no deal (bottom right). Certainly nobody modelled the scenario with the top left as a dominant outcome. Yet, with trust, it is nevertheless possible to arrive at a deal particularly if this is view as a win:win (or at least a compromise). There is plenty of material for discussion here.

	European Union
UK	Make Concessions	Hold Firm
Make Concessions	2,1	-3,3
Hold Firm	3,-3	-2,-1

Nash equilibria.

Three of these. In this scenario once a deal is struck, even a one sided deal, then there is no incentive for one side to unilaterally deviate. (both top right and bottom left – ie Boris deal and Barnier deal – are Nash equilibria). This leads to the speculation about both sides of chicken (for a analysis of this strategy for the UK side, see this critical analysis from @Usherwood or, for balance, a more sympathetic account )

	European Union
UK	Make Concessions	Hold Firm
Make Concessions	2,1	1,2
Hold Firm	3,-1	-2,-2

Barnier deals

Three of these. This is similar to the well-known Battle of the Bismarck Sea. By suggesting that the EU prefers No Deal to a Boris Deal, they now have a dominant strategy. Knowing this, the rational choice for the UK is to compromise, ending with a Barnier deal (top right). The same logic of course works in reverse to give a Boris deal as the likely outcome, though no teams predicted that (perhaps reflecting the demographic, remember I am not making any predictions or passing judgement!). This outcome arises if the either party believes that ‘No deal is better than a bad deal’. (of course if both parties believe that, then we are back to the prisoner’s dilemma).

	European Union
UK	Make Concessions	Hold Firm
Make Concessions	0,0	0,1
Hold Firm	1,-1	-1,0

We also discussed weak and strong dominance and the possibility of mixed strategies.

Please note, these are not my predictions nor do they necessarily reflect my (nor anyone else’s) wishes. It is merely an indication of how an assessment of payoffs can lead to different conclusions and therefore indicate a different strategic course of action. Of course, it will be fascinating to see how reality compares to these highly simplified analyses, but that is not the central aim of the exercise – it is about learning.

And in terms of learning outcomes, I was delighted how this example illustrates different game theoretic situations – weak and strong dominance, Nash equilibria, prisoner’s dilemma, mixed strategies, rationality …  so it definitely achieved its aim.

For those readers looking for a more in depth political analysis of game theory and Brexit, check out this 109 analysis by the IEA. For those looking for a decent introduction to Game Theory, there are many web pages and books available such as this Graphic Guide.

One final thing I should mention. This exercise would not have worked if students had not come to class prepared. This was achieved by a session earlier in the week where the students had completed a readiness assurance protocol (individual and team test followed by a debrief) as explained by the Team Based Learning Collaborative. The test covered pre-learning which was a series of six short (3-8 minute) narrated snippets, each culminating in a question to ponder (the answer to which is provided in the next snippet). I had also asked the student to play an online game “the evolution of trust” – if you haven’t played this, I strongly recommend it (and pay the author if you like it!), a deceptively simple game that ends up covering quite advanced topics in game theory – evolutionary stable strategies and recovery from ‘mistakes’ (engagingly called ‘copykitten’ in the game).

To conclude, I was really pleased with how this session went – the aim to not to ‘call’ Brexit correctly, but more about using something contemporary and familiar to explore some theoretical concepts in an engaging way. Not a bad outcome for a mere 2 hours of class time (both online).

For next year, I will have to find something else!