In this post, I attempt to apply a few of the theoretical concepts I’ve discussed in previous posts (on NonZeroSum.Games)to a field that we encounter often but remains a mystery to most of us - the stock market. If the stock market is a game, is it zero-sum? Who are the agents? What about rationality and higher-order beliefs? Exploring these questions below, I hope to unpack this topic through the lens of the human mind and common knowledge. But first …. 

What are Zero Sum Games? 

As the name suggests, a zero-sum game is one in which one player’s winnings are equaled by the other’s losses, resulting in no overall creation or destruction of wealth (Zero-Sum Games, 2019). If this is the case, we can see why the players have no common interests - mutual gain is impossible with diametrically opposing interests. Broadly, there are two kinds of zero-sum games : perfect information games, and imperfect information games. In a perfect information zero-sum game, like chess, both players are aware of the results of all previous moves. Importantly, in this kind of game there exists an optimal strategy, the minimax strategy, which may not ensure victory but definitely minimizes losses (Lecture 6 Zero Sum Games and the MinMax Theorem, 2017). Yes, chess does have an optimal strategy that can ensure a draw - but the sheer number of moves possible by each player at each stage make it impossible to determine currently. In imperfect information zero-sum games, players do not have the knowledge of past opponent moves - potentially because they occur simultaneously, such as rock-paper-scissors.

The Stock Market as a Game

Financial markets, including the stock market, have usually been classified as zero-sum. However, this is far too simplified a view of this game with millions of players - not just investors buying securities, but companies, shareholders, a board of trustees etc. (Brown, 2012). While some transactions can probably be classified as zero-sum, such as options or futures where a contract is written between two players and one wins at the expense of the other, other transactions are more subjective. Let’s revisit our definition above. Our definition necessitates no creation or destruction of wealth, but the stock market has clearly grown in overall value with time and economic growth, as companies have seen increased revenues and profits. What does this entail for people looking to get into the market? To understand this, let’s understand the difference between … 

Trading vs Investing

Once again, we meet our old game theoretic friend - time period. Just seems to come up in every post doesn’t it? Here, it’s essential to distinguish between trading (short-term buying and selling) and investing (long-term buying, and often holding, of shares). While trading more closely resembles a zero-sum game (with its short-term nature and regular trades), investing is often non-zero sum with the market reporting, on average, a 10% increase annually over the last century (Royal & O’Shea, 2024). Trading often relies on technical analysis, determining entry and exit points by analyzing graphs and candlestick patterns over different time frames. On the other hand, investing relies on fundamental analysis, exploring a company's value prospects and profitability in the long term (thus requiring patience). Neither is right or wrong, but trading certainly involves a higher degree of both skill and luck, while investing requires a repeated game mindset of a high discount factor.

Higher order beliefs 

The arguments so far have all assumed the only thing driving a stock’s price is the company’s overall “value”, but this is far from the truth. The stock market, like any other market, is still driven by consumer demand, and by extension of this by consumer beliefs. Then, as a rational investor, our strategy should factor in others’ beliefs. Why stop there? If our strategy depends on what others believe, and players are rational, then wouldn’t their strategy also depend on their belief of what others’ strategies would be? This repeats infinitely, a phenomenon known as higher order beliefs that every good investor should factor into their trading strategy.    

Behavioral Considerations 

Due to its large number of participants and stakeholders, it is perhaps best to view game theory’s analysis of stock markets in terms of probabilities, understanding the likelihood of human behaviour to be as we expect. Perhaps adopting a crowd psychology approach, thinking why someone would do the opposite of what you’re thinking of doing could change your viewpoint, eliminating confirmation bias. This reminds of one of the greatest debating techniques I’ve learned - steelmanning. You take your opponent’s strongest viewpoint, understand its validity, and factor this into your own rationale. Who knew a technique combining debate, game theory and behavioral economics could make me a better investor?

REFERENCES

Allen, F., & Morris, S. (2005). Game Theory Models in Finance. Kluwer Academic Publishers EBooks, 17–48. https://doi.org/10.1007/0-306-47568-5_2

Brown, A. (2012, September 18). Exploiting Game Theory for Profit in the Stock Market : Networks Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090. Cornell.edu. https://blogs.cornell.edu/info2040/2012/09/18/exploiting-game-theory-for-profit-in-the-stock-market/

Lecture 6 Zero Sum Games and the MinMax Theorem. (2017). https://www.cis.upenn.edu/~aaroth/courses/slides/agt17/lect06.pdf

Royal, J., & O’Shea, A. (2024, May 3). What is the average stock market return? NerdWallet. https://www.nerdwallet.com/article/investing/average-stock-market-return

Zero Sum Game (and Non Zero Sum). (n.d.). Corporate Finance Institute. https://corporatefinanceinstitute.com/resources/economics/zero-sum-game-non-zero-sum/

Zero-Sum Games. (2019). Stanford.edu. https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/zero.html