After my apocalyptic forecasts for 2012 in last month's column, I thought that we should shun the real world a little and look at some theories - but theories that have definite application in everyday life.
It has struck me recently that we are all stuck in a variety of games: from the Euro debt crisis, to trying to maximise the selling price of cement, from being married to the same person for decades, to deciding to pay - or not pay - your taxes. Many of these situations can be described using 'game theory,' perhaps better termed 'interactive decision theory.' This branch of mathematics (and philosophy and biology) can suggest the optimum strategies to follow in order to maximise your outcome or the outcome of everyone in the game - the two situations not always being the same.
The classic problem stated in game theory is the Prisoners' Dilemma (PD): "Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal - if one testifies against his partner, and the other remains silent, the betrayer goes free and the silent man receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail on a minor charge. If each testifies against the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept quiet. What should they do?"1
Robert Axelrod in his book 'The Evolution of Cooperation' (1984) suggested that in multiple-round games always testifying or always staying silent is not the most effective way for the men to reduce their own penalty. It turned out that a strategy that combined 'niceness,' retaliation, forgivenness and not being envious was the most effective. Presuming the other fellow to be honourable, and not likely to testify against you has initial benefits (especially if he does the same). Occasionally retaliating (by testifying) keeps the other prisoner 'honest,' but falling back to a trusting state through forgivenness will pay dividends in the long term. It is pointless, in this scenario, to be jealous of how the other prisoner is doing overall - you must only look out for yourself.
How does this apply to the current situation we find ourselves in at the moment, I hear you ask? Well, the point is that we all depend on others playing the 'game' according to the rules. If the rules change, (or we can change the rules) the possible outcomes will shift.
Cement producers wish to maximise their profits - which is not necessarily done by maximising their selling prices. If they can maximise the tonnage of products with the highest margins, that may be sufficient. Competitors may benefit from producing completely different products (oil-well cement, or sulphate resistant cement, perhaps) to avoid price competition. Members of a legal cartel can boost their profits by 'stealing' market share from other members or by selling under a pre-agreed minimum price.... but if everyone does it, the agreement collapses and everyone loses. The authorities want illegal cartel participants to testify (for which they may receive absolution) - a classic Prisoners' Dilemma.
Similarly, if you have a 25% market share and your competitor starts to build a 5Mt/year cement plant which will reduce your share of production capacity in the country, should you join the 'arms race' and build a plant as well, even if there is no demand for its production at the moment? (I have India in mind). Experience suggests that the companies that build the greatest amount of capacity do not necessarily turn out to be the most profitable in the long term - particularly when the market turns down and the company with the largest capacity has the largest overheads and the largest amount of unused cement production capacity. Perhaps it is best to only respond to real cement demand and to lag behind the market a little, maximising profits through scarcity of production.
Climate change is another case in point: All countries may benefit from reducing their emissions, but no country wants to be first to reduce them, so that no-one takes any action and everyone continues to suffer.
In the same way, the current Euro Crisis is a form of PD: the weaker EuroZone states don't want to change their ways, and they want to be bailed out by the stronger members of the Zone. The stronger members of the Zone (Germany and France, for the moment), don't want to bail out the weaker members, because if they do, the weaker members won't change their ways, and will just keep on doing what they have always done. However, if they don't bail them out (or authorise the ECB to bail them out) then not only will the weaker members of the EuroZone go bankrupt: everyone will be much worse off. The present course seems to be to change the rules of the game: but it may be that treaty change will take years.
It's difficult to see a win-win outcome to this game.
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