Shall we make some profits? (Game Theory and the Stock Market)
As we learned in class, game theory is ubiquitous in our lives. We can use game theory to guide our daily strategic decisions. So why not use game theory to generate positive returns on the stock market as well? Well, we should use game theory to maximize our financial success. In fact, “A Fundamental Game Theory Concept That Every Trader Should Understand”, is a brilliant article that concisely explores the game theory of investor sentiment(link: http://www.businessinsider.com/ben-hunt-on-the-sentiment-game-2013-11).
The article states the stock market decisions everyday investors or speculators make in terms of different investment strategies and different players(investors)(in game theory format). The central thesis Hunt made is that traders should successfully predict the investing decisions of other players and then, based on those decisions, choose profit maximizing strategies for themselves. This game theory discussion is rather complex because of the large amount of players and different types of players(investors, Federal Reserve, governments, corporations) as well as the sheer amount of strategies(buy, short, hedge, limit orders, stocks, bonds, real estate) in the stock market. This is in contrast to value investing, which theorizes that investors should not give too much weight to other investors’ opinion of stocks.
In class, we discussed the concept of dominant strategies and strictly dominant strategies. However, those are rather difficult to decipher since other players in the stock market have so many options. In turn, it is unlikely that one option or strategy consistently leads to the highest payoff(definition of a dominant strategy). An intuitive way of thinking about the author’s thesis is that if you account for the actions of other players in the stock market, you can in turn select the best strategy(strategy with the highest payoff) for yourself. In response, I believe game theory only helps investors at certain times. At other times, it can complicate the process or not even be able to suggest a best response or Nash equilibrium. To elaborate on this idea, I have created a simple possible stock market scenario below. I have attached the table.
The scenario is as follows. Suppose you are deciding whether to go long or short on Tesla( NASDAQ: TSLA) with a holding period of 6 months( you are a short-term investor). If you decide to go long and the majority of other investors(in terms of investment capital and investor population) go long as well, you both will profit. If you agree with overall market sentiment, you will profit in the short-term as you can see by the table. However, if you disagree, you will lose in the short-term. Even in this simple scenario, there is no pure strategy Nash Equilibrium or dominant strategy. Your profits depend on how well you can predict the investment decisions of the majority of other investors but of course, the stock market and its investors are hard to predict. Nash Equilibrium, as we learned in class, are outcomes where no investor would want to change his/her strategy. It very much makes sense that there is often never a Nash equilibrium in the stock market, and that is why the stock market is so volatile and fast-paced. After all, the stock market is a place people go for profit and not equilibrium. Indeed, following this model gives us insight into why the stock market is highly unpredictable. Game theory can however, in some situations, can make it easier to interpret and understand.
For instance, there is a mixed strategy equilibrium in this situation. Let us assume q is the probability that majority of investors will go long and 1-q is the probability they will go short. Then, let us assume p is the probability you will go long and 1-p is the probability you will go short. Solving out this scenario, we can figure out that the mixed strategy equilibrium is that you go long half the time and the majority of investors go long half the time. Even though, this situation and Nash Equilibrium is not particularly telling, other situations could be of use to help you profit in the stock market.
Some definitions to consider:
Nash Equilibrium– is a pair of strategies that are best responses to each other
Dominant Strategy–a strategy is a dominant strategy if it is a best response to every strategy of the other player(s)
In case, you cannot see the chart clearly, the outcomes are as follows:
(10,10) (-20,40)
(-20,40) (10,10)
