Game Theory's Relevance to Investing: The Basics

January 25, 2015 By in Game Theory Tags: ,

In many ways academia is no more immune to politics and arrogance than Wall Street. A great example is the view taken by pure mathematicians, who study abstract concepts regardless of real world applicability and think of their subject as intellectually uncontaminated as opposed to physicists, who think they are masters of the universe because they can understand it. This is a shame as it has created unnecessary barriers to the integration of mathematics as a useful tool for businesses and investors.

Physicists have had greater success, possibly due to their interaction with the real world in terms of such facets as flight, space travel, nuclear power, etc. However, the absence in the business world of other areas related to math has created market shattering fiascos such as Long Term Capital Management and the Doom’s Day Formula. In this post I’ll explain why and what to do about it.

The problems that physicists try to solve have to do with attempting to model real world problems: Brownian motion which is the movement of particles, how air acts as it moves over a wing, how to create controlled solid state combustion for space flight. These models are then transplanted to business and investment areas. Indeed, Brownian motion is the basis for the infamous Black-Scholes option pricing model.

The central pillar of such models are probability models. The central weakness is the very same probability models. When a probability model works in describing a real world problem it can be like magic. Think  of supersonic flight. The problem with probability based models in finance and business is that the particles (or people) are not supposed to change their behaviour. Unfortunately humans do all the time.

The limits of probability distributions to deal with human behaviour where recognised early on and several other approaches were attempted to compensate for this. The most famous is game theory as popularized by the movie “A Beautiful Mind.” Game theory basically does not assume a probability distribution and surprisingly still results in some extremely important results relevant to economics. The goal of game theory is to minimise the decision maker’s maximum regret, i.e. reduce the maximum pain. This mimics human behaviour surprisingly well.

A great example is quality improvement, in particular the fantastically marketed Six Sigma. Six Sigma packages basic quality improvement ideas together and then strongly advocates for their use. According to Wikipedia, the first point in Six Sigma’s doctrine is: “Continuous efforts to achieve stable and predictable process results (i.e., reduce process variation) are of vital importance to business success.” What doesn’t seem to be explained is why it is vital. The answer lies in reducing process variation (minimising) the maximum number of defects (regret). Simple.

For a wonderfully written, and mathematics free, exposition on the game theory of brands see What game theory can teach us about brands.

Important as the previous step is it still has shortfalls. The main one is that mathematical game theory is descriptive, i.e. it is more interested in understanding the problem and the existence and description of a solution rather than being prescriptive, i.e. how to develop and deploy a solution. The second failure is in terms of setting up the main explanation as the Prisoner’s Dilemma problem, which is quite famous and you can find by doing an internet search or wait until the next article in the series, but is less than useful as it focuses on a situation we normally don’t face: a prisoner faced with the decision of whether or not to  betray a colleague.

A far better example is the rent or buy problem. Imagine you decide to try golf as a hobby. You are faced with the decision of renting your golf clubs or buying them. Of course it makes sense to initially rent, as you don’t know if you will enjoy the hobby. But at what point does it make sense to buy? Buy too early and you might stop playing golf soon after, thus wasting money and causing regret. Wait too late to buy and you will wast money renting when you could have bought and this too will cause regret.

This same problem is repeatedly seen in business: how long to lease equipment, be it a factory, a generator or heavy trucks, before you buy? In terms of personal investments the classic is renting a home versus buying a home. How many people have spent sleepless nights on this problem just because they where never taught the tools to be able to reason about it?

For financial investments a core problem is when to sell losing stocks (do it too early and you might miss a rally that reduces your loss, which would cause you regret) and when to sell winning stocks (do it too late and the stock price might fall, causing regret at the missed profit). This explains the non-optimal behaviour of investors who sell their profitable positions early and keep their losers for a long time.

The previous article in the series on the art of bluffing strategy introduced the idea of mixed strategies. In the next article, we look at how game theory can thwart The Joker, save the good citizens of Gotham and make Batman irrelevant.