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...

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