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Measuring Utility: not as easy as we’d like

At the heart of economics and game theory lies the notion of the utility function. Without this concept, it becomes meaningless to attempt to logically deduce the optimal strategy for a situation. We often treat the utility function as a known quantity. Not only that, but we often assume that it is a constant value or a similarly logical, predictable function for a given outcome. When dealing with real people that have not seriously studied and analyzed their however, this is often a bad assumption to make.

For example, in the classic Prisoner’s Dilemma,  we assume that the goal of the criminals is to minimize their time in prison and thus the dominant strategy for each player is to confess (defect), even though the socially optimal set of strategies would be for each player to not confess (cooperate). We then saw if we modified the payoffs so that the players also cared about how much time their partner would have to spend in prison, we could make the dominant strategies to be for both players to not confess (cooperate) and thus coincide with the socially optimal outcome. This set of views for the prisoner’s dilemma game is artificially simplistic though. I imagine that in applications of the concept to more mundane situations than going to prison the payoffs would be even harder to nail down.

Humans are by default driven by fickle emotions and then attempt to rationalize their actions after they have already arrived at their conclusions. Only through a sustained conscious effort are able to act in a logical manner. Look at the various network bargaining games we discussed. For a three node network of A–B–C, the only logical decision for A and C to make is to always accept whatever B offers them. But, as we saw with the in class polling, every person has a different point at which they would reject the offer just out of spite. So we then modify the payoffs to account for feeling bad about being taken advantage of. That still doesn’t allow us to predict the outcome of the game and the optimal strategies for each player. Why? Because if you asked the same person multiple times, you would get multiple answers. Their payoffs depend how they’re feeling at that point in time and innumerable psychological factors ranging from what the other person looks like, the room the game is played in, what they had for breakfast, and so on.

Moreover, payoffs for seemingly objective scenarios (would you rather have $0 or $1) differ from person to person in a way not yet fully understood. The first article I have listed below talks about how cooperation and a sense of fairness is incorporated into most, but not all, peoples’ decision making process. The second article I have listed below talks about how simply varying the time given to make a decision varies one’s payoffs between greedy and cooperative. Subjects given less time to make decisions were more cooperative than subjects given longer to think about things. If things as small as the time to make a decision can profoundly impact the utility functions for players in a game, it seems that we should thoroughly analyze the payoffs for each player of a game beyond the logical payoffs. To do this is of course prohibitively difficult in many situations. So in conclusion, the results of game theory should be best thought of as a rough starting point outside of only the most heavily analyzed and expertly played games.

However, one of the most heavily analyzed games is investing in the stock market.  Huge amounts of time and resources are spent trying to get one’s investments to perform as well as possible. But, as discussed in the book A Random Walk Down Wallstreet, this is all a waste. The author (and economics professor), Burton Malkiel claims, based on the efficient market hypothesis that the best strategy is to simply pick a broad set of stocks according to major indexes such as the S&P 500, Russell 5000, and DJIA. He systematically explains from both theoretical perspectives and huge amounts of actual data that many common strategies can’t and don’t work.

The two major strategies people often use in investing are technical analysis and fundamental analysis. The strategy of looking at the past ups and downs of stocks, referred to technical analysis or “charting” fails because the stock market is large enough to where you won’t be able to capitalize on information already incorporated into stock prices. Everybody is already trying to play the dominant strategy (set of stocks to hold). But in order for stocks to be good to hold, you have to see that they’re good before everyone else does and the price rises accordingly. The strategy of fundamental analysis (which is what the professionals on Wallstreet typically use) involves looking at the “fundamentals” of a company or simply how strong you think their financial position, market position, and future plans are. This strategy fails because again, everyone is already analyzing everything and trying to make the best stock picks. You essentially have to predict random events, which is, by definition, impossible. Furthermore, the irrational psychological aspect is at play. The correlation between what are objectively the best stocks and the returns they produce are historically extremely weak. The myths amateur investors use as their strategies are too numerous to list here, but they all add another layer of unpredictability to the performance of stocks. When logical professional investors are aware of these effects, they become reluctant to pick stocks that they don’t think could appeal to market as a whole.  Thus we end up with bubbles such as the NYSE tech bubble of the early 2000s and undiscovered companies that never reach a high value. The historical data show no exploitable trend based of these facts.

The game of investing in the stock market shows how a simple logical analysis is not enough to determine the best strategy to play. Between the irrational psychological factors at play and the unpredictability of the other players’ strategies, game theory clearly must be used with caution. And yet, the data support the efficient market based strategy of buying and holding the whole market. From looking at all of this, I think that game theory is a great tool to analyze situations with, but we must remember its limitations. The assumptions we use are not small ones and we must try to account for the errors produced when interpreting our results. Furthermore, we should try to make sure we have truly captured all of the possibilities and complexities of the game itself before turning the mathematical crank of what the most logical strategies are.

http://www.nature.com/nature/journal/v489/n7416/full/489374a.html

http://www.nature.com/nature/journal/v489/n7416/full/nature11467.html

http://www.amazon.com/Random-Walk-Down-Wall-Street/dp/0393340740/ref=pd_sim_b_1

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