What does the 'two-thirds' game explain about financial markets?

Published in The Sunday Times on December 3rd 2023.

Are you familiar with the 'two-thirds' game? It’s a classic for many psychologists, game theorists and behavioural economists. Pick a whole number from zero to 100, which represents your best guess of two-thirds of the average of all numbers chosen by others in this game.
 

Before reading on, consider this - what is everyone else going to do?

You might start by realising that 50 would roughly be the average answer if everyone picked a random number — and then calculating that two-thirds of 50 is 33. But if everyone picked 33, then 22 would be the winning answer. In testing, many people go one step beyond the obvious and give answers around 20.

The question is why more people don’t keep going: two-thirds of 22 is about 15, and two-thirds of 15 is 10, etc. Eventually you get to zero. Zero is the Nash equilibrium which Economics Nobel prize winner, Richard Thaler, described as “the number that, if everyone guessed it, no one would want to change their guess.” In a world of hyper-rationality, the answer to this game would be zero. 

But instead of reaching this equilibrium, people instead display ‘k-step’ thinking. Someone who guesses randomly is a zero-step thinker. For most people, ‘k’ is a small number: 1, 2, or maybe 3. It’s not natural for most of us to think multiple steps ahead.

Keynes’ beauty contest 

John Maynard Keynes proposed a version of this as a model of the stock market. He described a newspaper contest where photographs of 100 faces were displayed. Readers were asked to choose the six prettiest. The reader whose list of six came closest to the most popular of the combined lists of all readers would be the winner. 

The best strategy, Keynes noted, isn’t to pick the faces that are your personal favourites, it is to select those that you think others will find prettiest. Better yet, he said, move to the “third degree”. This involves picking the faces you think others will think, that others will think, are prettiest.

The goal in stock market investing, according to Keynes, is not necessarily to pick the best company. It is to pick the company that others think will be the best company. Or the company that others think, that others think — and so on. 

The Keynesian Beauty Contest is an early theory in behavioural finance that describes how our perceptions of value can cause irrational fluctuations, in supposedly rational systems. It describes how short-term stock market fluctuations are not caused by changes in underlying value, but instead, by investors attempting to figure out what others think the “average investor” finds valuable.

Soros and reflexivity

The concept of reflexivity that George Soros popularised goes a step further. His theory proposes that there are feedback loops between investors’ perceptions of reality and the underlying fundamentals of an asset. Put simply, if you believe that others will invest in a stock and increase its price, this can initiate a positive feedback loop which actually makes the stock more valuable. In the context of the 2021 frenzy surrounding GameStop, it’s hard to argue with this thesis. Its price appreciation may have been a mirage, but it enabled GameStop to issue stock at inflated prices and, ignoring whatever it did with that capital, increase its value.  

Financial markets have more in common with biology than physics

For decades, I’ve been trying to figure out, with disputable success, how financial markets work. At the Kilkenomics festival some weeks ago, one particular session caught my interest. Traditional economic theories view the economy through the lens of physics which has immutable laws. But what if the economy, speakers argued, behaves more like biology, adapting, adjusting, and mutating as it goes? I think this is the correct way to think about financial markets.  

The 'two-thirds' game provides a useful framework to consider its workings. It’s possible to reason your way to the “correct” answer, but victory is still not guaranteed. We all reason differently.

Financial markets evolve through the interactions of human beings with all of their foibles. Very few iterations of the 'two-thirds' game are going to result in an equilibrium outcome - zero. Trying to second-guess what others are going to do is a strategy very few can claim consistent success at. George Soros is a notable exception – but I can think of precious few other names that belong in that pantheon. 

Keynes’ investing track record bears scrutiny. He struggled early on as he was trying to win the ‘beauty contest’. Eventually, he shifted his focus away from attempting to time market trends. In doing so, he essentially discovered value investing - consistently outperforming the market by embracing uncertainty and seeking out stocks where pessimism made prices fall below their inherent value. All investing is value investing at the end of the day – buying at a price that you think undervalues the business. 

Concentrate on your own behaviour and ignore the ‘two-thirds’ game

The investing world has moved on an awful lot since Keynes’ day. However, human nature hasn’t changed much, if at all. You can try to outguess others, as you might in the 'two-thirds' game. Or you can try to ignore the machinations of the game and focus on the things you have control over. In my experience, real life success at investing has far more to do with behaviour than analysis. Don’t try to predict the behaviour of others – focus solely on your own. 
 

Gary Connolly is Investment Director at Davy and can be contacted at gary.connolly@davy.ie or on twitter @gconno1.