The Quiet Game

Commentary by Dr. James McCann, Chief Scientist, Plotinus Asset Management

The news that business-chat company Slack Technologies was purchased for $27.7 bn caused a stir. However, given that its valuation in 2019 was $20bn, it was not a huge shock to the system. All the same, it exposed the question of how to value technology stocks.

According to one theory, such a purchase is conducted with full disclosure and information, but it is still a game of negotiation. Whether you are buying a tennis racket on eBay, or a billion-dollar enterprise, this is where the obscure mathematics of game theory enters the argument. Game theory has been notoriously used to model problems ranging from global thermonuclear warfare to cattle auctions.

The first ideas sprung from a book by John von Neumann and Oskar Morgenstern in 1944. The Theory of Games and Economic Behavior, which was an effort to apply mathematics to markets. von Neumann was beyond brilliant in the exact sciences of physics and mathematics, in which the laws of nature are well-defined.

In business… randomness plays a role certainly, but it is the behavior of other participants in the game this is more unpredictable.

A learned astronomer can play with charts and figures at leisure. In business, life is more complicated and much more interesting. Randomness plays a role certainly, but it is the behavior of other participants in the game that is more unpredictable. Worse than that, there is not a set of instructions or even a rule book. Games such as Chess or Go are not like stock investments, they have “perfect information:” each player and any outside observer (or computer) can see everything and even calculate the best moves. Even a modest chess “engine” can outplay all but the best players. And now even, Go has fallen to the power of Deep Mind.

Before 2015 there were no good Go-playing computers, partly due to the computational complexity of searching all possible sequences of moves. There are countless scenarios. The main obstacle seemed to be the “lack of intuition” and “strategic foresight” that comes with experience and knowledge. A top-ranked Go player can visualize patterns emerging from each potential move and the opponent’s reaction, assuming “rational play.”

The stock market game is rather more complicated. There are many competing players, each with their own strategy, and not necessarily rational in their behavior! By way of illustration, on one hand we have the “efficient market hypothesis” which implies that the actual price is the true price. There is no benefit on buying or selling an asset. This contradicts reality, in which investors often make irrational and systematic investment errors. On the other hand, we have “herd behavior” in which investors act as a group, but without external direction, in feeling or buying behavior, by copying others in the group. This anti-subjective idea follows Keynes beauty contest in which peer opinion is more highly valued than one’s own. The two contrasts are “everyone knows everything” (or equivalently “no one knows anything”) and “a few people are in the know.”

A more common form of “herd following” is choosing a fund manager with a stellar track record. Herding has a bad reputation because it is blamed for bubbles and crashes. Furthermore, we have “trend following” in which prices that have recently increased tend to continue to move up, while falling prices tend to decrease over a certain time, and this time can be extended by “herding.” Mathematically this is a recurrence relation, relating the past to the future. When trend following works it is in contradiction to the efficient market!

Can game theory ever be applied to a free-for-all such as capital markets. Well only in the following sense. When there are very many participants in the game one can lump them all together as a single average player with a fluctuating temperament. By average, the definition is statistical average. In physics, this is also the case if you are tracing an electron path through a wire as it gets buffeted by the vibrating atoms in the copper lattice, and in such a case one uses a “mean field.” So, in a world of brokers, scalpers, and spreaders, it is best to play the quiet game.

December 2020

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