Latticework of Mental Models: Game Theory

Every time I get into my car, the thought of crossing the “dead-circle” sends a shiver down my spine.

“Dead-circle” is the name that I have given to the intersection near my house. It’s a small intersection with no traffic lights and rarely managed by any traffic police. What scares me most about this intersection is that it doesn’t need a lot of traffic to invite a gridlock situation.

A traffic gridlock is so frequent in that junction that I have started calling it the dead-circle. Throw in four five cars, couple of two wheelers and you have the perfect recipe for a jam.

In the first few minutes of traffic jam the whole area drowns in the echo of incessant honking. In another few minutes you find few restless drivers rolling down their windows and shouting at each other.

I feel very bad for the people living near that intersection. Poor victims of a serious case of negative externality.

What’s interesting is that just like stock market, greed and fear rules the behaviour in traffic jams. Everybody is either scared of staying stuck in traffic (even if it’s only for 5 more minutes) or greedy about saving another 5 seconds by not giving way to another fellow.

Given an option between offering the way to another car and zooming past shamelessly, most people go for the latter. It’s as if they are trying to cross a collapsing bridge.

If they just let one car pass turn by turn, the traffic would flow smoothly. By being selfish some cars do manage to save few seconds but it’s not uncommon to find the offending driver getting caught right in the middle of the gridlock. Overall the gridlock ends up wasting time for many other commuters.

The example shows what’s best for you, the individual (or a small group), may not be best for society (or a larger group). This brings us to the an important idea from the discipline of Economics. It’s called Game Theory.

Game theory deals with what happens when individuals or groups of people interact with one another to achieve their goals. Unless you really understand game theory, you can’t begin to actually understand human behaviour.

The best way to understand the concept of game theory is to look at the problem of prisoner’s dilemma. Let me take Peter Bevelin’s help in describing this problem. Peter, in his masterpiece book Seeking Wisdom, writes …

Suppose you and a partner commit burglary. Both of you are picked up by the police who then question you one by one. There is not enough evidence to convict you unless one of you confesses. The interrogator gives you a choice to cooperate or not.

• If you both deny the crime, there is still enough evidence to put you both in jail for 1 year.
• If you both confess, you both go to jail for 3 years.
• If you confess but your partner denies, you will be free and your partner will go to jail for 10 years.
• If you deny but your partner confesses, you will go to jail for 10 years.

What should you do? The consequences for you depend on what your partner does. From an outsider’s perspective, it seems that both of you would be better off denying the crime (1 year). But from your point of view, it seems best to confess (freedom). The problem is that you don’t know what your partner will do. If your partner betrays you, it is better that you also betray him and get 3 years in prison, instead of the 10 years you get if you deny, but your partner ends up confessing. If on the other hand your partner denies, it is still better that you confess because this way you will be free, instead of the 1 year you get if you deny.

Since both you and your partner follow this “logic” and confess, you will both go to jail for 3 years. Doing what you believe is in your best interest leads to a worse outcome than if you cooperate and deny. But here is the dilemma. You don’t know if you can trust your partner. Cooperation only works if you and your partner can trust each other.

Same logic holds in the traffic gridlock situation. If you let the other guy go first (akin to denying), you can’t trust that the next guy will let you pass (confess). So a rational response is to confess i.e. be greedy and selfish in crossing the intersection.

As an aside, some of you might remember the movie A Beautiful Mind, which was based on John Nash’s life. John Nash won the nobel prize in economics for making important contributions to game theory.

Let’s explore how game theory gives us insight into the world of business, investing and other areas.

Game Theory In Business

In a competitive market, each firm is so small compared to the market that strategic interactions with other firms are not important. In a monopolized market, strategic interactions are absent because the market has only one firm. So when it comes to understanding the monopolistic or competitive markets, game theory isn’t much useful.

But game theory becomes particularly interesting in oligopolistic market, where there are two or three equally strong players. Because each firm knows that its profit depends not only on how much it produces but also on how much the other firms produce. In making its production decision, each firm in an oligopoly should consider how its decision might affect the production decisions of all other firms.

In their paper, Avinash Dixit and Barry Nalebuff, use the example of Pepsi and Coca-cola to explain how game theory works in business.

The prisoner’s dilemma has applications to economics and business. Consider two firms, say Coca-Cola and Pepsi, selling similar products. Each must decide on a pricing strategy. They best exploit their joint market power when both charge a high price; each makes a profit of ten million dollars per month. If one sets a competitive low price, it wins a lot of customers away from the rival. Suppose its profit rises to twelve million dollars, and that of the rival falls to seven million. If both set low prices, the profit of each is nine million dollars. Here, the low-price strategy is akin to the prisoner’s confession, and the high-price akin to keeping silent. Call the former cheating, and the latter cooperation. Then cheating is each firm’s dominant strategy, but the result when both “cheat” is worse for each than that of both cooperating.

Game Theory and Arms Race

It’s estimated that US alone has a stock of weapons and ammunition which can destroy the planet earth many hundred times over. Same with other countries like Russia. Why do these countries keep manufacturing weapons? Game theory, Dixit and Nalebuff say, has answers –

Arms races between superpowers or local rival nations offer another important example of the dilemma. Both countries are better off when they cooperate and avoid an arms race. Yet the dominant strategy for each is to arm itself heavily.

Yuval Harari, in his brilliant book Sapiens,  connects biology and game theory in an interesting way. He writes –

Game theory explains how in multi-player systems, views and behaviour patterns that harm all players nevertheless manage to take root and spread. Arms races are a famous example. Many arms races bankrupt all those who take part in them, without really changing the military balance of power. When Pakistan buys advanced aeroplanes, India responds in kind. When India develops nuclear bombs, Pakistan follows suit. When Pakistan enlarges its navy, India counters. At the end of the process, the balance of power may remain much as it was, but meanwhile billions of dollars that could have been invested in education or health are spent on weapons, yet the arms race dynamic is hard to resist. ‘Arms racing’ is a pattern of behaviour that spreads itself like a virus from one country to another, harming everyone, but benefiting itself, under the evolutionary criteria of survival and reproduction. (Keep in mind that an arms race, like a gene, has no awareness – it does not consciously seek to survive and reproduce. Its spread is the unintended result of a powerful dynamic.)

Game Theory In Investing

In the context of investing, no one can explain game theory better than Buffett. He wrote in his 1986 letter to shareholders –

Over the years, we had the option of making large capital expenditures in the textile operation that would have allowed us to somewhat reduce variable costs. Each proposal to do so looked like an immediate winner. Measured by standard return-on-investment tests, in fact, these proposals usually promised greater economic benefits than would have resulted from comparable expenditures in our highly-profitable candy and newspaper businesses.

But the promised benefits from these textile investments were illusory. Many of our competitors, both domestic and foreign, were stepping up to the same kind of expenditures and, once enough companies did so, their reduced costs became the baseline for reduced prices industry-wide. Viewed individually, each company’s capital investment decision appeared cost-effective and rational; viewed collectively, the decisions neutralized each other and were irrational (just as happens when each person watching a parade decides he can see a little better if he stands on tiptoes). After each round of investment, all the players had more money in the game and returns remained anemic.

Conclusion

The Game Theory mental model is useful in understanding not just the traffic gridlock but a host of other problems in Economics, Biology, Political Science, Computers, Poker and even why people arrive late.

So far we have looked at about thirty mental models from various disciplines. Teaching is a nice hack for learning and my own understanding has improved a lot while teaching these mental models.

A wise man once said, “The school education will help you earn a living, but self education will make you a fortune.”

The problem with traditional education system is that they too good in doing what they were designed to do  i.e. to mass produce skilled workers who would become very efficient cogs in the wheel.

But once you realize the limitation of such education, you will naturally gravitate towards the idea of self education.

Self education starts the day when you start designing your own study curriculum. A curriculum which doesn’t get over in few semesters; where there are there are no grades (except the one you award yourself) and no project submission deadlines (excluding the ones you set for yourself).

I actually don’t like the word deadline. Live-line sounds much more exciting. Because it’s the time you give yourself to inject life to the learning process. The quest for multidisciplinary learning is serious but not dead-serious. 🙂

Charlie Munger’s prescription for seekers is to start by learning the big ideas from the big disciplines. And self education is the only way to gradually become wiser in worldly affairs.

If you’ve been following the Latticework series, I would say you’re already on the right track to acquire the worldly wisdom.

Take care and keep learning.