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The Prisoner’s Dilemma

The name prisoners dilemma comes from an earlier version of the game that involved true prisoners jailed for jointly committing a crime. Each of them had to decide if to remain quiet or inform on his partner.

An equilibrium point

I’ve always found that story a bit confusing contrived. So let’s just stick with the real world example. In the hockey example the players will inevitably end up not wearing helmets that pair of choices is known as an equilibrium point, since neither player has incentive to change their choice unilaterally you.

You shouldn’t think of an equilibrium point as something that represents the optimal set of choices. The players would be better off if they both wore helmets in this case. You should instead think about equilibrium point as a stable set of choices, it’s a set of choices from which no one has any incentive to deviate on their own.

For hockey players, if your competitors are wearing helmets then you’re only going to make yourself worse off by starting to wear one. Not all social interactions involve direct competition, in many cases small groups of people do best when they coordinate their behavior, especially when their interests are aligned.

Think about your own social interactions. Often you in your social partners both want the same outcome and when one person does well the other person also does well. When you and your friends meet at a movie theater with 20 screens each could choose any of those 20 movies, but you’d rather go to the movie together then go to separate movies.

Cooperation depends on mutual trust

So you discussed your preferences and you end up seeing a movie you all enjoy. Coordination introduces its own set of challenges for decision-making. Consider the following example: a group of hunters are working together to trap a stag in a forest. They each enter the force from different directions and walked toward the center forming a shrinking circle around the stag.

As long as they all work together stag can’t escape in the each share in a big reward, but there’s other game the forest small hares are plentiful and easy to catch. If one of the hunters decides to go after a hare instead that hunter will be sure to get a small reward, but the stag will be able to escape from the trap.

In a game like this if every player cooperates they’ll all get a large reward, but if at least one person doesn’t cooperate and takes a sure small reward then all the rest will get nothing. So, cooperation depends on mutual trust. If everyone trusts the others in the system works well, but once trust breaks down the system breaks down.

This probably seems familiar to you: many of our economic institutions rely on shared trust and when that trust falters there are runs on banks collapses of industries and other tears in her economic fabric. Game theory is very powerful because it can take complex real-world problems like helmet wearing a hockey or trust and economic institutions and reduce those problems with simple models that can be solved mathematically.

Behavior doesn’t always follow the predictions

But, like the other models we’ve considered throughout this article game theoretic models require assumptions about how people should behave. Some of the basic assumptions are consistent with the rules for behavioral economics experiments they introduced in an early article:

  1. players should be rational, they are motivated by their own outcomes,
  2. players should think that other,
  3. players are rational to players can’t communicate during the game and can’t collude to split their payoffs after the game and
  4. there aren’t any sort of hidden external influences that are represented in the games explicit outcomes.

These are the basic assumptions and modern game theory relaxes those assumptions in many ways that are well beyond the scope of today’s article, but by assuming that players are rational that they consistently follow their self-interest game theorists can find solutions to games that explain complex real-world problems.

People’s behavior doesn’t always follow the predictions of game theory. In particular, people can’t always think through all the steps of how their choices should influence other people’s choices which should influence their own choices and so on. That problem “I know that you know that I know and so on” is known as a backward induction.

In principle, a rational player should be able to perform as many steps of backward induction as possible to reach an optimal decision, but we can’t. Let’s see why by considering decisions and markets were value depends on what other people are thinking, like in the stock market.

In 1936 the economist John Maynard Keynes described the business of picking stocks in unflattering terms, saying that “professional investment may be likened to those newspaper competitions in which the competitors have to pick out the 6 prettiest faces from 100 photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole”.

In this conception, the most successful investors are those who can accurately assess the general sentiment of other investors and then stay one step ahead of the rest.