Collective well-being and individual interest do not always go hand in hand. This spontaneous assertion is illustrated perfectly in the famous “prisoner’s dilemma” formalised in 1950 by US mathematician Albert Tucker who was head of the Princeton University Maths department for 20 years.

Two prisoners are arrested together but questioned separately. They can either remain silent or denounce their partner in crime. Depending on their response, a number of outcomes are possible:

Case 1: if one of the two prisoners “rats out” the other, that prisoner is freed while the other obtains the maximum prison sentence of 10 years.
Case 2: if both prisoners betray each other, they are both sentenced to a lower prison term of five years.
Case 3: if both refuse to betray each other, they obtain the minimum sentence each (six months).

Amateurs of game theory will have recognised one of its most famous illustrations: even in the case where it is in the interest of both players not to betray the other (Case 3), the fear of finding themselves harshly penalised if the other chooses a different response is likely to cause each prisoner to betray the other.

This theory, widely developed by John Forbes Nash, an unusual US mathematician (1), has a number of implications in the study and competitive positioning of companies and another illustration of it can be found in recent political news.

Prisoners who denounce each other are now everywhere. Politicians denounce bankers as responsible for all wrong-doing; economists denounce states as irresponsible and expensive whereas in France, the left and right-wing parties denounce each others’ respective errors. We are entirely in the Case 2 scenario whereby each prisoner acts in their sole interest and takes us far from the optimal solution. In a nutshell, the global economic situation is deteriorating even more quickly than if players cooperated intelligently.

One step further towards the models proposed by Nash comes the notion of cooperative or un-cooperative games. The case of the two prisoners is typically un-cooperative. If they consulted each other, they would certainly have a different reasoning. In contrast, in the corporate world, agreements on prices reflect a cooperative game that competitions authorities aim to punish for the good of consumers.

So what about the public realm? While the system remains a cooperative one in that we are able to vote or even leave the game, the reality is clearly far more nuanced however. The government imposes its rules, as shown by the current multiplication of tax measures that are “un-cooperative”. As such, it is pretty much certain that we are heading for an un-cooperative prisoner reaction, rational for each individual and yet generally absurd in view of the extent of the deficits to be paid for.

Taxpayers, like the prisoner, are only seeking to minimise the maximum sentence depending on the rule imposed. Overtaxing one type of revenue or another is therefore set to cause a significant erosion in the said revenue depending on the way the victim adapts. In so doing, the state is simply increasing the individual sentence while reducing the collective interest.

A very costly public homage to John Forbes Nash… or a concrete validation of the Laffer (2) curve, the mathematical illustration of the popular saying that quite rightly reminds us that “too much tax kills tax”!

with the assistance of Marc CRAQUELIN

(1) John Forbes Nash (born in 1928) suffers from schizophrenia…
(2) US liberal economist born in 1940