Playing with game theory
Ever wondered why the airline industry cant make any money? Why it pays to bluff in poker? Or even why the Wallabies had to suspend Lote Tuqiri for the deciding Bledisloe rugby test? The answers lie in a fascinating area of economics called game theory.
People have been devising 'optimal strategies' ever since Ugblatch and Ramblok the cavemen successfully evaded a sabre-tooth tiger by stripping off their smelly under-hides, lobbing them in a bush and running in opposite directions. But this strategising was largely a matter of educated guesswork until 1928, when the eccentric Hungarian mathematician John von Neumann wrote his first paper on the subject of 'game theory'. With the paper, von Neumann created a whole new branch of mathematical study and revolutionised the world of economics.
How is it, von Neumann asked, that a poker player who knows how to bluff will always beat one that simply plays by the percentages? The answer, he posited, is that poker isn't about winning the most hands, but winning the most money. And, if you simply play by the percentages, all your opponents will know when you have a good hand and refuse to bet against you. By bluffing on occasion, you introduce an element of uncertainty and, despite losing the odd hand, you encourage your competitors to think about betting up big when you have that elusive royal flush.
Von Neumann's paper was an attempt to find the optimal bluffing strategy. Ever since, game theorists have been analysing different scenarios where participants interact, trying to determine the best strategy and most likely outcome.
MAD policy a little too crazy
The Cold War nuclear stand-off between the US and the USSR brought game theory out of academia and into the mainstream. Both sides followed a MAD policy (mutually assured destruction): if you drop a bomb on me and blow up half the world, I'll drop a bomb on you and blow up the other half. The problem, game theorists argued, was that the threat was merely that and, once the first bomb was dropped, it wasn't in anyone's interest to destroy the remaining half of the world. The logical conclusion being that, if anything, it's best to get it in first.
The only way the MAD policy could work would be to have an automatic retaliation mechanism that the other side knew about – if you drop a bomb on me there's one coming your way whether I like it or not. It doesn't quite work like that in reality, but it does bring us to Lote Tuqiri's suspension for not turning up to training.
As every young sporting star knows, it doesn't matter how many threats the coach throws at their team about the consequences of not attending Tuesday's fitness session, come Saturday morning no-one wants the team's best player sitting on the sideline. Inevitably, he ends up in the thick of the action, wins the game and, along with the second-best player, doesn't turn up to training next week either.
The only way to put a stop to this destructive cycle is for coaches to have their own automatic retaliation policy. A guarantee that if you don't train, you don't play – whether the coach and team like it or not. The Wallabies might suffer against the All Blacks next weekend, but for the longer term Tuqiri's suspension makes a lot of sense.
The airline industry's bad economics
The simplest game theory scenario is a situation called Prisoner's Dilemma. Substitute prisoners with a couple of airlines and you'll soon see why the economics of the airline industry are so poor.
Imagine that you're running Singtas Airlines and I'm heading up Qanpoor. We're the only two airlines competing in our market and the one decision that we have to make for the year is whether we'll lower prices or not. If we both keep our prices as is, we'll both make $400m profit for the year. If you lower your prices and I don't, all the customers will flood to Singtas; you'll make $600m and I'll just break even (and vice versa). If we both lower our prices, we keep sharing the customers but we only make $200m each. The payoffs are represented in the table below.
Game theory in the airline industry | ||
Qanpoor lowers prices | Qanpoor maintains prices | |
Singtas lowers prices | Both make $200m | Singtas makes $600m Qanpoor breaks even |
Singtas maintains prices | Singtas breaks even Qanpoor makes $600m |
Both make $400m |
Obviously, the best place for us combined is in the bottom right-hand corner. We both maintain our prices and both make $400m. But consider it from an individual point of view.
If I lower my prices, you'll make nothing if you don't lower your prices, and $200m if you do. Obviously, you want to lower your prices as well. If I maintain my prices at current levels, you're faced with a $400m profit if you maintain your prices, or a $600m bonanza if you lower them.
Sub-optimal solution
Put simply, no matter what I do your best course of action is to lower your prices. Look at the scenario from my perspective and I come to the same conclusion, so we both end up with lower prices and lower profits.
In the jargon it's known as a Pareto sub-optimal solution. You don't need to know much about the economist Vilfredo Pareto, but sub-optimal describes the economics of the airline industry perfectly.
Real life is never so simple and when the scenarios are played repeatedly, the strategies become a lot more complicated. But game theory is a very useful tool for understanding businesses and markets. Hopefully you've found this introduction useful. If nothing else, just remember von Neumann's tip: it pays to bluff occasionally.