Brexit is often described as an economic game-changer,
whilst Prime Minister Theresa May has accused the Scottish First Minister of
playing a game with her call for a second Scottish independence referendum. But
politics is a form of game and Brexit certainly warrants examination in a game
theoretic context, which can be described as “the study of mathematical models
of conflict and cooperation between intelligent rational decision-makers.”
Leaving aside the question of the rationality of the Brexit decision, we can perhaps
use it to gain some additional insight on what the optimal (or least
sub-optimal) outcomes are likely to be, not only for the UK but also for the
rest of Europe.
Mathematical games can be split into two broad categories: cooperative and non-cooperative. Whatever the EU may be, it is a consensus based
institution in which decisions are traditionally arrived at in a cooperative
manner (although the Greeks may not see it in this way). In principle, the EU
is a cooperative environment in which players are constrained to act according
to the legal rules. Those who breach the rules are subject to sanctions. To
take the example of environmental protection, there were 3464 infringements of
EU law over the period 2007 to 2015, of which the UK accounted for 179, or 5%.
Italy was the biggest offender accounting for 9% of all infringements followed
by Spain (8.6%) and Greece (7%). Without making any judgement on individual
nations’ degree of compliance with the law, the rules are known and the EC
publishes data to name and shame the transgressors who are expected to comply
with sanctions.
Similar rules apply to trade. But not everyone thinks the EU
applies the rules consistently. Alan Halsall owns a company (Silver Cross)
which makes prams, and in 2015 the French government banned his company from
selling its products in France on safety grounds despite being cleared for sale
elsewhere across the EU. Not surprisingly, Mr Halsall argued strongly in favour
of Brexit. But the problem is not the EU rules: it is that the French
government applies higher safety standards than other countries. In fact, Mr
Halsall had a case for applying to the European Commission to appeal this
decision although he chose not to do so, arguing that he will benefit more from
applying his energies to markets where he is able to generate sales.
But if he thinks the current rules are stacked against him, Brexit will change the rules of the game
completely. The process of renegotiating trade deals with the rest of the
EU implies entering into a non-cooperative bargaining “game” where the EU has
no incentive to cooperate with the UK, primarily because it wishes to avoid
giving support to the idea that leaving the EU is an easy option. Although the
ultimate outcome is likely to result in a cooperative situation in which a new
set of rules apply, the process of getting there will be non-cooperative. And
even if we do reach a cooperative solution, the end result is likely to produce
an outcome which is worse than the position we started from. In game theoretic
terms, the outcome will be inefficient – at least for the UK.
Those of you who have seen the film A Beautiful Mind will be
aware of the work of John Nash, who offered significant insights into the
mathematics of bargaining problems. His key insight was that equilibrium is
reached when no player can unilaterally change their strategy and get a better
result, given that they know the strategy of the other player(s). In other words two parties should cooperate
when non-cooperation leads to results where at least one side is worse off
(so-called Pareto inefficient outcomes). Clearly, the EU is not going to allow
the UK to have free access to the single market: such a strategy will weaken the
EU because it implies there is no cost to exit, which will endanger the EU’s
long-term existence. But the UK cannot accept access to the single market whilst
continuing to pay into the EU budget and accept ongoing free movement of labour
(the Norwegian solution), because this gives the UK the same system as before
Brexit but without any control over the legislative process.
The problem the EU faces is to trade off punishing the UK
against the harm that non-cooperation inflicts upon itself. Likewise, the UK
must trade off the best deal against the political costs of giving away
too many concessions. Abstracting from deals regarding the exit costs, one
possible Nash equilibrium is for the
EU to offer the UK continued access to the single market for an annual fee
which is lower than the UK's current net EU contributions but which offers no say over
drafting legislation. The UK should accept this because although it is a worse
deal than the current arrangements, it is economically less damaging than
relying on WTO tariffs and preserves market access for exporters on both sides
of the table.
One of the best known forms of game is the zero sum option. Many Brexit supporters
appear to believe they are operating in a positive-sum game: if the UK leaves
the EU, any disadvantages from leaving will be more than offset by the gains.
There is no evidence to support this sunny optimism. Indeed any action which
harms UK trade with the rest of the EU, such as the imposition of trade
tariffs, will result in a negative sum outcome.
Looking at this in a wider perspective, it is evident from
recent polling evidence that the degree of dissatisfaction with the EU is
rising across the whole continent. We can thus perhaps think of the decision of
whether to leave as a sequential game,
in which the action of one country influences the decisions of others. It is yet
possible that the UK’s decision to be the first mover in this game will trigger
other countries to go down the same path. But it is not in the UK’s interest to
be the first mover because it will face all the adverse consequences as a
result. Far better in this case to allow others to make the first move – this
may be a game where there is no first mover advantage.
Contrary to what politicians tell us, Brexit really is a
game – admittedly one with high stakes. However, a central assumption in many
variants of game theory is that the players are rational. In other words, they always
choose an action which gives their most preferred outcome, given what they expect
their opponents to do. I have a pretty fair idea how the European Commission is
likely to act: Based on recent rhetoric I am less certain of the rationality of the British position.
