Penalty shootouts offer businesses a valuable insight into the power of game theory. Photo / Thinkstock
Penalty shootouts offer businesses a valuable insight into the power of game theory. Photo / Thinkstock
As we play host to the biggest football tournament ever to hit these shores, Massey University Economics Professor Christoph Schumacher and Masters student Nigel Espie have a look at what football can teach business.
There are few moments in life that possess the tension of a penalty shootout during a play-off match at a FIFA World Cup. Across the previous five Under 20 FIFA World Cups, 25 per cent of play-off games were decided by penalty shootouts. If the tournament in New Zealand follows a similar path, we can expect several nerve-wracking moments over the coming weeks.
Arguably, the most important player in a penalty shootout is a team's goalkeeper. Some teams recognise this by substituting a specialty shootout keeper onto the field in the closing stages of a match if the scores are level. These goalkeepers say their prayers and perform special rituals, all while watching for cues as to where the striker is going to shoot.
If penalty shootouts represent a critical factor underpinning the success of a football team, is there an optimal strategy for the defending goalkeeper? And what lessons are there for businesses in this way of thinking?
The branch of economics known as game theory brings together elements of mathematics, statistics, and psychology to predict how people will behave in strategic situations or games. Much of the credit for its high profile must go to the film A Beautiful Mind, which depicted the life of the Nobel Prize-winning game theorist John Nash, who died recently in a car crash.
Seen through a game theory lens, a penalty shootout is a game that involves two players - the striker and the keeper. To simplify matters, let's assume that both players have three options. The striker can choose to make their shot to the right, centre, or left of the goal. Similarly, the keeper can elect to dive to the left or right, or defend the centre of the goal.
Nobel Prize-winning game theorist, the late John Nash. Photo / AFP
Let's also assume the striker is equally good at taking shots to all three areas in the goal and the keeper is equally good at saving balls kicked to the three sections of the goal. So what would be the best strategy for a goalkeeper in this situation?
With no past knowledge of the striker's penalty history, you would expect the striker to randomly select their shot. Game theory would suggest that the best option for the keeper is to also randomly select an area of the goal to defend. This maximises the likelihood of saving a goal while preventing the opposing team from discerning any preference by the keeper.
However, the reality is that most strikers' shots will not be perfectly random. Instead, strikers may have a slight preference for one area of the goal over other areas. This preference may arise through superstition or simply because the striker is better at scoring into one particular area of the goal.
In the 2006 FIFA World Cup quarterfinal between Germany and Argentina, Jens Lehmann examined a piece of paper stored in his sock before each Argentinian player came forward to take his penalty kick. It's always been assumed each striker's historic kicking habits were written on the paper, helping Lehmann save two of the four penalty shots taken.
Let's take a look at what may have been going through Lehmann's mind after receiving information about the striker's preferences. He would know that for right-footed strikers who are historically more successful at taking penalty shots to the right of the keeper, it would pay to dive to the right more often than the centre or the left. Game theory suggests that, when facing a striker like this, diving right around half the time and covering the centre and left around a quarter of the time each would increase the keeper's chances of a save by 10 per cent.
Game theory offers a powerful way of thinking about various strategic situations - but the uses of strategic thinking stretch far beyond football. Game theory is widely used in business in areas such as product pricing, contract negotiation, and competitive strategy.
Another interesting insight from game theory is that despite the striker being better at shooting to the keeper's right, the striker should actually target this side less frequently because that is what the keeper expects.
Game theory offers a powerful way of thinking about various strategic situations - but the uses of strategic thinking stretch far beyond football. Game theory is widely used in business in areas such as product pricing, contract negotiation, and competitive strategy.
To see this, consider the following example. Two rival competitors selling official Under 20 FIFA World Cup merchandise are both looking to open new stores on Queen Street in Auckland. The firms are the only two selling the merchandise but both know that the proximately to customers and the other competitor will determine their overall profitability. Both firms need to attract the largest number of customers into their store rather than that of their competitors if they want to make as much profit as possible.
Christoph Schumacher, Professor in Economics and Innovation (left) and Nigel Espie, Masters student at Massey University.
Let's assume that more customers shop at the bottom of Queen Street and progressively fewer customers shop in upper Queen Street. Since the competitors are selling the same merchandise, consumers have no preference for either store and will purchase from the store closest to them.
So where is the best location along Queen Street for the firms to establish a shop presence? For the given example, game theory suggests that both firms will locate in the central most location along Queen Street. In doing so, both firms have optimised the amount of customer thoroughfare for their shops.
The results of this example can be seen in numerous real-world examples. Have you ever wondered why different supermarkets, petrol stations or home improvement stores typically set up shop very close to each other? Wouldn't it make more sense to be located away from their competitors? Through strategic thinking, these stores know that although being close to one another will result in direct competition, it is still best to be in the most populated locations at the centre of people's attention.
There are an endless number of other situations for which game theory and strategic thinking can be applied. For example, what is Burger King's best option once it knows that McDonald's is going to launch a new burger? If you believe a share market bubble is going to burst within the next year, when is the best time to sell your stocks? What should Samsung do if Apple decides to lower the prices of all of its iPads?
Penalty shootouts offer businesses a valuable insight into the power of game theory. Through employing strategic thinking, goalkeepers can develop the optimal strategy for saving penalty goals. Similarly, with game theory, a company can better navigate itself through its market and develop a competitive advantage by out-thinking its competition.
Christoph Schumacher is a Professor of Innovation and Economics and Nigel Espie is a Masters student at Massey University.
