How can we make good decisions under uncertainty, and what typical mistakes do people make in real life? We joined one of the exciting sessions of Researchers’ Night at Corvinus. In one of the classrooms of the Gellért Campus, both young children (primary school pupils) and elderly ladies tried their hand at the Hotel board game. As Nóra Felföldi-Szűcs and Kata Váradi, lecturers at the Institute of Finance, explained, this decades-old game is a very effective way of simulating risky financial and economic decisions that often occur in real life. 

The aim of the game is to build hotels with an initial capital of 12,000 dollars. Players can earn income from other participants who “stay overnight” in their hotels, and at the beginning, there is also fixed external financing. To build a hotel, both luck and capital are needed: if you land on the right square and have money, you can buy a plot, and later you can start construction. The winner is the one who survives the longest without going bankrupt. In the game, the dice carry the risk: where will we land, and where will the opponent land? At any moment, luck may strike and you may land on a square that grants a free building – but will you manage to roll a five next time to avoid all the paying squares? 

At certain points in the game, Felföldi-Szűcs explains how mathematics and probability theory can be used to measure and model risk, and how players can analyse possible scenarios. “What could happen to me and with what probability? How can probability theory help me model risks? Our university students learn these methods, and many already practice them while still at university. For example, many are interested in the crypto markets, but they need to understand the risks behind the fact that in the past Bitcoin investors could observe annual returns of as much as 1,400 percent,” she notes. This is essential knowledge in real life too, when making financial decisions. If someone’s capital is in an equity fund, then instead of dice rolls, real market risk factors, economic indicators, and interactions between markets shape the share prices of listed companies. 

“When we measure risk, we want to know how much of a surprise we might face compared to the expected value. The standard deviation measures the extent of deviation from this expected value,” the lecturer explains. 

Decision Dead Ends 

One graduating student, Máté Horváth from the Insurance and Financial Mathematics master with Csege Csató and Benedek Czövek from the business informatics bachelor’s program even calculated whether the outcome of the Hotel game depends on who plays first. The answer: yes – the starting player has a decisive influence on the final result. The game is also used in university teaching. “It helps students better understand and supplement the material. According to their own feedback, they can grasp financial dilemmas more clearly this way than if they only studied the textbook,” says Felföldi-Szűcs. Dice are also used in teaching probability theory at university, helping students a lot in the introduction to the subject. Coin-tossing examples can even lead directly to binomial option pricing models. 

Another question is whether our thinking in real life is truly rational, adds Felföldi-Szűcs. For example: suppose there is a person who loves reading, is quiet, wears glasses, and really likes books – what is more likely, that this person is a librarian or a shop assistant? The majority vote for librarian. In reality, it is statistically more likely that the person is a shop assistant, since there are many more of them. Here the incorrect answer ignores statistical probability. 

And here we arrive at some typical “decision dead ends” (in technical terms, heuristics). It is common for people, in uncertain and risky situations, to simplify or speed up decisions and behave irrationally. For example, we have all encountered the “anchoring” method, when we make a not entirely rational consumer decision as a result of comparing the crossed-out higher price with the discounted one. 

The workshop also highlighted that these very problems were studied by psychologist Daniel Kahneman and Amos Nathan Tversky, a major figure in decision theory. For this work, Kahneman was awarded the Nobel Memorial Prize in Economic Sciences in 2002 (by then Tversky had already passed away; the prize was shared with Vernon L. Smith). Their joint result, the so-called prospect theory, opened the way to a unique dialogue between psychology and economics, which, enriched by the work of others, led to the emergence of behavioural economics. 

Katalin Török