How can game theory help you?

This is how Wikipedia defines Game Theory:

Game theory is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.

What is a game? A game is any interaction between multiple people in which each person’s payoff is affected by the decisions made by others. (Source: SciShow). That is, the outcomes of decisions are inter-dependent.

For example:

  • Company A and Company B are competitors – they make widgets
  • These widgets are undifferentiated products.
  • Currently, both A and B have 50% share each in the market.
  • Company A wants to grow market share – so, it cuts the prices of its widgets by 20%.

Do you think, A is going to grab market share from B? Of course we know it can’t. A’s action is going to invite a price cut from B as well, matching 20%. What is the end result?

Both A and B will retain the same market share, but at much lower profit margins. In this example, A’s decision was not independent, but it was inter-dependent. ‘A’ should have anticipated similar action from ‘B’. This is a ‘game’.

A well known example of application of game theory is “prisoner’s dilemma“:

  • A and B committed a crime together, and have been arrested by the law enforcement.
  • They are locked and interrogated in separate rooms. They can’t communicate with each other.
  • The prosecutors make an offer to the suspects – “if you confess, we’ll let you go free, and imprison the other guy for 3 years”.

How will each suspect behave in this situation?

Let’s look at the choices A and B have. There are four possibilities:

  1. If A and B confesses: each will serve 2 years in prison
  2. If A and B remain silent: each will serve 1 year in prison
  3. If A confesses, and B remains silent: A will be set free, B will serve 3 years in prison
  4. Like (3) above, if B confesses, and A remains silent: B will be set free, A will serve 3 years in prison

prisoners-dilemma_choice-picture

But, think from each person’s side. Let’s take A:

  • A does not know what B thinks.
  • A is not sure whether B will confess or deny.

A is looking at his options, and trying to decide whether he should deny or confess:

  1. If A denies,thinking that B will also deny – and then actually B confesses – A will end up in jail for 3 years. B will go free. This is unacceptable for A.
  2. If A confesses, while B doesn’t – A can go free.
  3. If A confesses, and while B also confesses – both will end up in jail for 2 years.

So, in (1), A is worse off, and hence unacceptable. (2) & (3) are better from A’s standpoint. It is better for A to confess. He will be better off in any case, compared to (1). B’s thinking process will also be same.

However, note that both A and B are collectively worse off here. If they had co-operated, they would have to spend just one year in jail. But, since they cannot communicate while in custody, they cannot co-operate. This is an example of application of game theory in co-operative situation.

There are two branches of game theory:

  1. Co-operative: everyone agree to work towards a common goal – like coalition or cartels. The focus is on collective actions and payoffs. Here, game theory tells you how to be fair.
  2. Non-cooperative: which means competition – business or social situations. The focus is on individual actions and payoffs. Here, game theory tells you how to be smart. Individually, players are better off when they are in ‘Nash equilibrium‘ – a state where it is better for them to make no moves, as any further action will not result in any benefit. In the prisoner’s dilemma example, it is better to remain in the collectively worse off situation – if any person denies, he will spend 3 years in jail, compared to 2 years in Nash equilibrium. Smart, isn’t it?

In business

As I explained in the first example, price cuts by competitors in undifferentiated businesses tend to result in players ending up worse off. It is better for them to co-operate, than to compete.

Hence it is not uncommon for companies in similar businesses to collude and maintain high prices, so that they retain high margins. For example, telecom companies might collude and charge high prices for voice calls and data. This is the reason why most countries have competition commissions which look at whether anti-customer practices are being followed by market players.

OPEC is the most famous example for co-operative game theory. Except during 2014-16, the countries in this cartel used to determine how much to produce, so that they can keep prices high.

Co-operation is possible only if there are only a few players in the market – that is, if it is an oligopoly. In a monopoly, however, a question of co-operation does not arise. In a highly competitive industry – with a lots of players, or players who do not trust each other – cooperation is near to impossible.

In investing

In investing, we need to keep in mind how players in various industries co-operate, or compete, so as to have a better view of the competitive landscape.

Warren Buffett wrote this in his letter to shareholders in 1985:

“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… 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.

…Burlington (Industries, the largest U.S. textile company) made a decision to stick to the textile business… During the 1964-85 period, the company made capital expenditures of about $3 billion, far more than any other U.S. textile company… A very large part of the expenditures, I am sure, was devoted to cost improvement and expansion. Given Burlington’s basic commitment to stay in textiles, I would also surmise that the company’s capital decisions were quite rational… Nevertheless, Burlington has lost sales volume in real dollars and has far lower returns on sales and equity now than 20 years ago… each share commands about one-third the purchasing power it did at the end of 1964. Regular dividends have been paid but they, too, have shrunk significantly in purchasing power.”

I recently read a research report, in which one of the reasons why the analyst liked a particular stock was this: “The fact that these moves are being followed by all competitors (big and small) reinforces the opinion that it is getting its mojo back”. The company spent some time and money, and made some strategic moves, and ultimately the competitors just imitated it. What’s the point? I don’t understand the analyst’s pitch.

In a way, contrarian investing is also an application of non-cooperative (competitive) game theory. You first understand where all the other market participants are going, and how they will bid prices up. And then, you take an informed contrarian view – for example, by investing a sector which is now out of favour, thereby taking advantage of low prices.

In life and career

Students pursuing the same course: Every now and then, a particular career path (say, MBA) is in favour, and students pursue them in herds. In such a situation, as a student, you should purse some other course – because, in the future all these students will graduate and vie for the same kind of jobs. This will be a disadvantage in terms of supply-demand mismatch where there are limited job openings and high supply of graduates. You should go for a course that is less in favour, to stand a chance of getting reasonably good salary. Understand what others are doing, and act to your advantage.

Farmers doing the same crop: When a particular crop output rises in price, farmers rush to cultivate the same crop. What a farmer should keep in mind is that, other farmers are doing exactly what he is doing, and in the future supply of this crop could outstrip demand – leading to a price crash. Again, understand what others are doing, and act to your advantage.

Games: like chess and poker where we need to anticipate the other player’s moves.

Here are some video lessons. I particularly like the SciShow one (very comprehensive).


Sources:

Wikipedia: Game theory

SciShow: YouTube channel

Avinash Dixit and Barry Nalebuff: Game theory, Prisoner’s dilemma

Khan Academy: Nash Equilibrium

Berkshire Hathaway: Warren Buffett’s letter to shareholders in 1985

Featured image: Pixabay


See MILE’s Mental Models page


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