When a person studies mathematics at ordinary level, they might be led to think that its content can be easily replaced by a calculator. But mathematics is much more than calculations. Any decision involving logical thinking requires mathematical skills.
Decision Theory is one example. Let’s say you check the weather forecast and because the weather is fine, you decide to spend a day in Gozo. In this case, individuals make the best decision based on their understanding of the world.
In Game Theory, another criterion comes into play: if the weather is fine, others will also want to spend the day in Gozo, so better set off early. By anticipating how others will react, individuals reach the best decision.
The application of Game Theory is widespread around the world. It is applied in economics, diplomacy and military strategy. Game Theory includes a set of players such as business managers or companies that use different strategies in their undertaking while keeping game rules set in a hierarchy. It is assumed that all participants are already aware of the possible outcomes or results and they strive to achieve what is best for them.
A thought experiment in Game Theory is the ‘prisoner’s dilemma’ (see diagram above), originally formulated by American mathematician Albert W. Tucker in 1950.
Real life presents us with a surprising number of choices in any given day, ones that you must resolve through logic
Two prisoners, A and B, suspected of committing a robbery together, are isolated and urged to confess. Each wants the shortest possible prison sentence for himself; each must decide whether to confess without knowing their partner’s decision. Both prisoners, however, know the consequences of their decisions:
(1) if both confess, both go to jail for five years;
(2) if neither confesses, both go to jail for one year; and
(3) if one confesses while the other does not, the confessor goes free and the silent one goes to jail for 20 years.
The apparent best solution for them would be for each to confess and go to jail for five years. Paradoxically, however, the two robbers would do better if they both adopted the apparently irrational strategy of remaining silent and serve only one year in jail.
This intriguing hypothetical problem can be observed in real-life situations with similar characteristics, such as two shops engaged in a price war, nations competing in an arms race or farmers increasing crop production.
Real life presents us with a surprising number of choices in any given day, ones that you must resolve through logic. So you might be using more maths than you think!
Rona La Bella and Elaine Chetcuti are senior lecturers at the University of Malta Junior College.
• Balladares et al. (2023) found that board games which are not necessarily labelled educational, such as Snakes and Ladders, Monopoly and Othello, are very beneficial to children, helping them in improving skills such as counting, addition, and the ability to order numbers. Their methodology included holding game sessions on average twice a week for 20 minutes, over six weeks. The children involved, aged between three and nine years old, were facilitated by adults. Children’s skills were tested before and after the intervention sessions so that comparisons could be made. It was noticed that children’s skills improved significantly.
• Interested to learn more about science around us? Join the Junior College Mathematics Department and other groups at the Science in the City event in Valletta on September 29. This year, we will get to know about the changemakers through the ages and around us.
For more science news, listen to Radio Mocha on www.fb.com/RadioMochaMalta/.
DID YOU KNOW?
• What’s so mathematical about an A4 paper with a weird size of 210mm x 297mm? The A-series paper sizes have one thing in common: their dimensions are such that one side is the square root of two times the other.
• This ratio guarantees that when a paper is cut in half through the longer side, the ratio is maintained.
• A0 is a one-metre-squared paper with dimensions 841mm x 1189mm, half of it is the 594mm x 841mm A1 size paper, half of A1 is the A2 with dimensions 420mm x 594mm and so on.
• This clever way of standard paper sizes guarantees that when we scale our work by printing on an A4 instead of an A3, we do not lose the proportionality but it is simply scaled down by a factor of two.
For more trivia, see: www.um.edu.mt/think.