“Unlike engineers (or at least those on The Big Bang Theory), we cannot rely on some physicist to tell us exactly what it would take for a rocket to escape the earth’s gravitational pull. Economists are more like plumbers; we solve problems with a combination of intuition grounded in science, some guesswork aided by experience, and a bunch of pure trial and error.”
-Abhijit Banerjee [1]
Optimising versus Satisficing
How dependent are economists on the assumptions they make? In the words of Adam Smith, a rational man – ‘homo economicus’ will always act in a way that maximizes utility as a consumer and profit as a producer. As students of economics, we often come across terms like ceteris paribus to indicate a simplified set of assumptions, which will aid us in theory. However, the human mind works in mysterious ways, and we tend to make suboptimal decisions, deviating from classical economics. The concept of bounded rationality in behavioural economics helps explain this phenomenon. It contrasts with the notion of ‘homo economicus’ by acknowledging that individuals are limited by their cognitive capacity, the availability of information, and the urgency of decision-making. They often engage in satisficing- selecting the first option that meets their criteria rather than optimising- going for the best option within a given set of constraints.
Bounded rationality also explains the divide between the opinions of economists and the masses of people who trust economists about economics. Before the Brexit vote, UK economists urgently warned the public about the potential costs, but their concerns largely went unheeded. A 2017 YouGov poll in the UK revealed that only 25% of people trusted economists when discussing economics, placing them just above politicians, who were trusted by only 5%. In comparison, trust in nurses was 84%, and weather forecasters were trusted twice as much as economists.[2] A similar survey in the U.S. in 2018 found that again, only 25% of people trusted economists, with only politicians ranking lower.[3]
The Keynesian Beauty Contest and a Guessing Game
The Keynesian beauty contest, originally introduced by John Maynard Keynes in his 1936 book The General Theory of Employment, Interest, and Money, delineates how individuals should make decisions based on others’ perceptions rather than their preferences. He described a newspaper contest, where entrants select the six most attractive faces from a hundred photographs, with prizes awarded to those who pick the most popular choices. A naive strategy would be to choose the face the entrant personally finds most handsome. In contrast, a more sophisticated participant considers public perceptions of attractiveness, anticipating how others will make their selections. As Keynes noted, “It is not a case of choosing those [faces] that, to the best of one’s judgment, are the prettiest, nor even those that the average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligence to anticipating what the average opinion expects the average opinion to be.”
The following game extends this reasoning!
Imagine you’re sitting in an economics class. The teacher says “Think of a number between 1 and 100. Whoever guesses closest to 1/3rd of the average wins the game and gets an extension for their assignment”. The maximum average is 100 (if everyone individually chooses 100) and the minimum average is 0 (if everyone individually chooses 0). Simple mathematics tells us that the guess should lie between 0 and 33.33. Game theorists will apply the Nash Equilibrium and tell us (quite surprisingly) that the winning answer should be 0. Let’s look at why!
An economist at the first level of thinking would anticipate that since the guess should lie between 0 and 33.33, he should guess 1/3rd of 33.33 giving us 11.11.
At each level, economists think they’re the smartest since they want to maximize their utility, an economist at the first level does not know about the second level and thinks that they are at the deepest level of thinking.
An economist at the second layer of thinking, however, will know about the economist at the first level, and believe himself to be at the deepest level of thinking. The highest average now becomes 11.11 and the guess becomes 1/3rd of 11.11 giving us around 3.7.
Under classical economics, the final answer given by the Nash equilibrium is 0. Absurd, isn’t it?
Perfect rationality means players assume infinite layers of rational thought, where each participant expects everyone else to behave in a fully rational manner. In this ideal scenario, the common knowledge of rationality leads all players to ultimately converge on a winning guess of 0, as they anticipate that everyone will make the same logical deductions. In contrast, bounded rationality reflects the cognitive limitations and imperfect information that players face in reality. Under bounded rationality, participants cannot fully grasp the reasoning processes of others, resulting in guesses that deviate from 0. This limitation prevents players from reaching the Nash equilibrium, leading to a wider range of guesses based on heuristics rather than the optimal strategy. This stems from imperfect information. The crux of level k theory is that the smartest economist must correctly identify the level of thinking of others, neither more nor less, to win the game . Empirically, this level is around 2/3 for most classrooms. The more ‘perfectly rational’ the cohort of students, the nearer the winning answer will be to 0 and the higher will k, the level of thinking be.[4]
Price Bubbles and Focal Points
An application of level k thinking can be seen through price bubbles in financial markets as well. A price bubble occurs when the price of an asset rises significantly above its intrinsic value, driven by investor speculation and irrational exuberance.
In game theory, a focal point (or Schelling point) refers to a solution that individuals tend to choose by default to avoid coordination failure when they cannot communicate with each other. This concept was introduced by economist Thomas Schelling in his book The Strategy of Conflict (1960). Schelling posited that people often coordinate their intentions or expectations based on shared understanding, leading them to converge on a prominent option within their environment. For instance, in an informal experiment, Schelling posed the question of where two strangers might meet in New York City without prior communication. Most respondents suggested “noon at the information booth at Grand Central Terminal,” a location that, while not inherently superior to others, held cultural significance as a traditional meeting spot, highlighting its prominence as a focal point.
Investors may converge on certain focal points—often driven by prevailing market sentiment or popular trends—leading to a self-reinforcing cycle of increasing prices and this creates price bubbles. For instance, during the dot-com bubble in the late 1990s, many investors flocked to technology stocks based on their perceived potential rather than fundamental valuations. As prices soared, the behaviour of first-level thinkers, who were primarily motivated by the rising trend, created a focal point that attracted even more investors, further inflating the bubble. Ultimately, when the realization of overvaluation sets in, these bubbles burst dramatically, resulting in significant financial losses for those who were caught up in the hype, underscoring the importance of understanding market psychology and the dynamics of focal points in financial decision-making. A similar and more relatable effect can also be seen concerning the ‘hypebeast’ culture around sneakers, especially the Nike Air Jordans.
Financial Markets and Overvaluation
Price bubbles often lead to an overvaluation of the quantity. Howard Marks, co-founder of one of the largest hedge funds in distressed securities, has given the example that when a company reports good news about future profits, first-level retail investors will buy its shares based on that good news alone. However, a second-level thinker with more sophistication would argue that if everyone only buys in response to good news, then the good news becomes bad news because it overvalued the stock’s price, making it a bad choice.[5]Overvaluation is becoming a major problem in financial markets all over the world and it is important to be cognisant of level k theory.
The Buffet indicator is calculated by dividing the nation’s stock market cap by the GDP (Gross Domestic Product) of the nation. It was created by famous investor Warren Buffet and is based on the underlying principle of comparing the intrinsic value of assets to the speculated value. India’s Buffet Indicator is currently raising concerns, as noted in the Economic Survey presented in Parliament in July 2024, cautioning that a high m-cap-to-GDP ratio does not necessarily indicate economic growth or sophistication. Instead, it suggests that if the equity market’s claims on the real economy are excessively elevated, it may signal impending market instability rather than resilience.
“Significant interest from domestic and global investors in the Indian stock market as an attractive investment destination and sustained IPO activity placed the Indian market fifth in the world by market capitalisation in FY24. India’s market capitalisation to GDP ratio has improved significantly over the last five years to 124% in FY24, compared to 77% in FY19, far higher than that of other emerging market economies like China and Brazil. It is essential to strike a note of caution,” the report said.[6]
In cases of overvaluation, investors suggest that the price of these stocks be shorted.Short selling is an investment strategy where an investor borrows shares of a stock and sells them, hoping to buy them back later at a lower price. For example, if an investor thinks a stock currently priced at $100 will drop, they might borrow and sell the shares. If the price falls to $80, they can buy the shares back, return them to the lender, and make a profit of $20 per share. Level K thinking becomes extremely important here and its absence often leads to losses: during the dot-com bubble, for example, short sellers targeted overvalued tech startups, believing their prices would fall. As a result, when a startup was acquired at a price higher than its shorted stock value, short-sellers faced forced cover at inflated acquisition prices, resulting in substantial losses. By recognising different levels of reasoning among stakeholders, economists and investors can better anticipate market behaviours and trends, particularly in volatile situations, and we must all strive to be the deepest-level k thinkers out there!
Citations
[1]: Banerjee, A. V., & Duflo, E. (2019). Good economics for hard times. Allen Lane.
[2]: Smith, M. (2017). “Leave Voters Are Less Likely to Trust Any Experts — Even Weather Forecasters.” YouGov. Retrieved from https://yougov.co.uk/topics/politics/articles-reports/2017/02/17/leave-voters-are-less-likely-trust-any-experts-eve
[3]: Banerjee, A., Duflo, E., & Stantcheva, S. (2019). “Me and Everyone Else: Do People Think Like Economists?” MIT Mimeograph.
[4]: Zhou, H. (2022). “Informed speculation with k-level reasoning.” Journal of Economic Theory, 200, 105384. https://doi.org/10.1016/j.jet.2021.105384
[5]: Oaktree Capital. (2015). “It’s Not Easy.” Retrieved from https://www.oaktreecapital.com/docs/default-source/memos/2015-09-09-its-not-easy.pdf
[6]: Economic Times. (2024). “Harbinger of Market Instability: Economic Survey Warns Against Soaring M-Cap to GDP.” Retrieved from https://economictimes.indiatimes.com/markets/stocks/news/harbinger-of-market-instability-economic-survey-warns-against-soaring-m-cap-to-gdp/articleshow/111918846.cms?from=mdr
[7]: Hindenburg Research. (2023). “Adani Update: SEBI.” Retrieved from https://hindenburgresearch.com/adani-update-sebi/ and https://hindenburgresearch.com/adani/