Bounded Rationality

When working with economic models, we typically need to characterize the behavior of some agent or group of agents. An agent may be a consumer, an investor, a firm, or a government – essentially, a decision-making actor. So, to discuss an agent’s ability to make decisions, what should we assume about that ability?

These assumptions typically take the form of beliefs about the rationality of the agent(s). In different contexts, assumptions of rationality can take many different forms (and for an excellent in-depth overview of those contexts, read this piece by Tyler Cowen). For example, we may want to assume: consumers want to maximize the amount of satisfaction they receive from purchasing, given the amount of money they have to spend; firms want to maximize their profit; strategic players want to avoid playing strategies which are always worse than some other option.

Intuitively, rationality assumptions make sense – agents typically want to do what is in their best interest. Why would someone not make an optimal choice?

Well, in tic-tac-toe, finding an optimal strategy is easy. But what about checkers? Chess? Much more difficult! How about in choosing an optimal retirement plan when there are potentially hundreds or thousands of different ways to invest?  In many decision-making problems in economic models, discovering an optimal strategy for an agent requires solving complex mathematical problems it can take years of graduate school to fully understand and compute! Arriving at an optimal choice can be extremely difficult – is this really what we think individual agents are able to do when making real-life decisions?

The short answer is: realistically, no. This sentiment is most often expressed as the notion of bounded rationality. Individual decision makers are rational, but only up to a certain degree. People are not computers, and as such, do not have the ability to solve the way a computer can. Consider the chess example: computer programs designed to play chess can compute the consequences of dozens of actions many turns forward in the game – in a matter of seconds. What about the best human chess players in the world? They may:

  • only consider the responses to the most obvious actions taken by their opponents, since there are, at any time, many potential moves which can be taken;
  • only be capable of thinking ahead 4 or 5 moves from the current play.

The reasons for these “bounds” on a human player’s ability to analyze moves seem intuitive. As humans, we do not have enough foresight to think 25 moves ahead without tremendous effort. Nor can we account for every single option when there are dozens or hundreds which can occur. And importantly, even if we could, the effort and time required to complete such calculations cannot be afforded. There can be deadlines for choosing a retirement plan, and time restrictions on moves in a game of chess. In other words, even if everyone had sufficient knowledge of calculus and subgame perfection (and whatever other skills might be required), in practice, we frequently do not (or cannot) take the time to properly solve for what is best. [Sometimes this may be a result of an over-reliance on our intuitive way of thinking for an answer, even when a correct solution could easily be obtained with a little analytical thinking.]

And indeed, there is some evidence that human agents run up against the bounds of their rationality in situations where decision making requires complex analysis. One example of such research suggests (HT: Mark Thoma):

Dr Tobias Galla from The University of Manchester and Professor Doyne Farmer from Oxford University and the Santa Fe Institute, ran thousands of simulations of two-player games to see how human behaviour affects their decision-making.

In simple games with a small number of moves, such as Noughts and Crosses the optimal strategy is easy to guess, and the game quickly becomes uninteresting.

However, when games became more complex and when there are a lot of moves, such as in chess, the board game Go or complex card games, the academics argue that players’ actions become less rational and that it is hard to find optimal strategies.

This research could also have implications for the financial markets. Many economists base financial predictions of the stock market on equilibrium theory – assuming that traders are infinitely intelligent and rational.

This, the academics argue, is rarely the case and could lead to predictions of how markets react being wildly inaccurate.

This is not to say that assuming rationality in economics is not worthwhile. In making simple decisions, and given sufficient skills/time to compute, individuals can get it right. But it is important in practice to have realistic expectations on people’s ability to solve complex problems. Our ability to think rationally, as much as we may wish to believe the contrary, is not infinite.

Examples:

  • Gary Marcus describes this concept in the context of limits on human memory, but also touches on the broader theme of understanding our own limitations (hence the title of Cognitive Humility):

Hamlet may have said that human beings are noble in reason and infinite in faculty, but in reality — as four decades of experiments in cognitive psychology have shown — our minds are very finite, and far from noble. Knowing the limits of our minds can help us to make better reasoners.

Almost all of those limits start with a peculiar fact about human memory: although we are pretty good at storing information in our brains, we are pretty poor at retrieving that information. We can recognize photos from our high school yearbooks decades later—yet still find it impossible to remember what we had for breakfast yesterday. Faulty memories have been known to lead to erroneous eyewitness testimony (and false imprisonment), to marital friction (in the form of overlooked anniversaries), and even death (skydivers, for example have been known to forget to pull their ripcords — accounting, by one estimate, for approximately 6% of skydiving fatalities).

Here is research from Colin Camerer discussing the limitations of humans’ ability to play “rationally” in game theoretic applications. It includes research on how chimps often outperform human participants in game theoretic experiments, with respect to their ability to play Nash solutions.

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