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Thursday, August 30, 2007

The Illusion of Wealth

Imagine that one day you were greeted by your boss at work and told that you had been given a 100% pay rise because of your sterling efforts. Later that day, your bank calls to let you know that your savings and investments have doubled overnight due to an odd fluctuation in the international financial markets. But just when you thought that all your years of hard work had finally paid off, you discover when buying your groceries that evening that the price of food and drink has also doubled – but that does not matter too much, this is just a small increase.

Are you in a better position than you were the night before? Even taking into account the rise in your cost of living, your net savings have increased, so should you be thanking your boss and your bank manager?

Whilst you may feel wealthier in this situation, this is simply an illusion. You still have to work as many hours tomorrow as you did yesterday to buy your groceries – nominal values have risen, but not real values.

Economists have long considered that financial markets limit the impact of traders trading on nominal values – irrational traders. This is because it is assumed that they are taken advantage of by smarter traders. However, new studies by Jean-Robert Tyran of the University of Copenhagen have shown that there are situations in which money illusion can have a massive impact on the market, especially when there is a fall in nominal values.

An interesting example is the housing market. When interest rates are low, monthly nominal interest payments on mortgages are low compared to the rent on similar properties, so people start to buy. However, if inflation is decreasing, whilst current payments on the mortgage are falling, the real cost of future mortgage payments is increasing. This is because your salary is not growing and it will take you longer to pay off your debt. These investors have fallen for the illusion. They are similar to those who pay off their credit card bill with monthly payments over 24 months, instead of over 12, as the down-payments are smaller.

Tyran’s experimental studies show that if there is a monetary contraction within the market – that is, if the nominal costs of goods and services fall – firms are reluctant to follow suit and cut their prices as this would result in lower nominal profits, even if their real profit would remain the same.

This is called nominal loss aversion and results in part from the fact that our inbuilt fear of losses tends to outweigh our desire for a gain of the same amount. It can be seen in other financial areas, such as employees accepting a nominal pay increase, even if it results in a real pay-cut if it does not match inflation. Another example is a homeowner being more unwilling to sell a house at a real loss if it comes with a nominal loss rather than cloaked by a nominal gain.

Conversely, the experiments show that firms have no problem increasing their nominal prices should there be a rise in inflation and wages to maintain their real profit.

Laboratory work is often based on simplified economies, whilst interpretation of real data can be extremely difficult, so Tyran hopes that experimental research, combined with real observations of the market, can be used together to better understand money illusion.

posted by Plus @ 1:40 PM 2 comments

Wednesday, August 22, 2007

Listen to the first Plus Podcast!

If you enjoy stepping into the world of mathematics through the Plus website, now you can take maths on the move with you and enjoy Plus whereever you are! We are pleased to release our first Plus PodcastBreaking the ice: Maths reshaping geometry and combating climate change. In this podcast we talk to Shahn Majid about a whole new geometry of space, find out about how mathematics is combatting climate change, as well as all the latest news from the world of maths. You can subscribe to the podcasts, or just stay tuned to Plus for the next podcast due late September.

Happy listening!

posted by Plus @ 9:44 AM 0 comments

Friday, August 03, 2007

Game over for checkers

Computer scientists at the University of Alberta have solved checkers, the popular board game with a history dating back to 3,000 BC.

After 18-and-a-half years and sifting through 500 billion billion (a five followed by 20 zeroes) checkers positions, Dr. Jonathan Schaeffer and colleagues have built a checkers-playing computer program that cannot be beaten. Completed in late April this year, the program, Chinook, may be played to a draw but will never be defeated. The results of this research were published recently in the journal Science.

"This is a tremendous achievement — a truly significant advance in artificial intelligence," said Dr. Jaap van den Herik, editor of the International Computer Games Journal. "I think we've raised the bar — and raised it quite a bit — in terms of what can be achieved in computer technology and artificial intelligence," said Schaeffer, chair of the University of Alberta Department of Computing Science. "With Chinook, we've pushed the envelope about one million times more than anything that's been done before."

A self-described "awful" checkers player, Schaeffer created Chinook to exploit the superior processing and memory capabilities of computers and determine the best way to incorporate artificial intelligence principals in order to play checkers.

With the help of some top-level checkers players, Schaeffer programmed heuristics — rules of thumb — into a computer software program that captured knowledge of successful and unsuccessful checkers moves. Then he and his team let the program run, while they painstakingly monitored, fixed, tweaked, and updated it as it went.

An average of 50 computers, with more than 200 running at peak times, were used everyday to compute the knowledge necessary to complete Chinook. Now that it is complete, the program no longer needs heuristics — it has become a database of information that knows the best move to play in every situation of a game. If Chinook's opponent also plays perfectly the game would end in a draw.

"We've taken the knowledge used in artificial intelligence applications to the extreme by replacing human-understandable heuristics with perfect knowledge," Schaffer said. "It's an exciting demonstration of the possibilities that software and hardware are now capable of achieving."

Schaeffer started the Chinook project in 1989, with the initial goal of winning the human world checkers championship. In 1990 it earned the right to play for the championship. The program went on to lose in the championship match in 1992, but won it in 1994, becoming the first computer program to win a human world championship in any game — a feat recognized by the Guinness Book of World Records.

Chinook remained undefeated until the program was retired in 1997. With his sights set on developing Chinook into the perfect checkers program, Schaeffer restarted the project in 2001. "I'm thrilled with this achievement," he said. "Solving checkers has been something of an obsession of mine for nearly two decades, and it's really satisfying to see it through to its conclusion."

"I'm also really proud of the artificial intelligence program that we've built at the University of Alberta," he added. "We've built up the premier games group in the world, definitely second-to-none. And we've built up a strong, international, truly world-class reputation, and I'm very proud of that."

posted by Plus @ 4:23 PM 0 comments