Posts Tagged ‘ game theory ’

Overconfidence Advantages

Fortune favors the bold1 – and sometimes even the unreasonably overconfident, a new study says.

The rarely photographed ritual by which penguins impress their potential mates.

Using a mathematical model of simulated competitors, researchers found that while overconfident strategies don’t always win, their wins tend to be bigger than those of more cautious opponents. The total rewards they reap often make up for their losses – and then some.

The researchers think this may have to do with differing responses to novel situations, and the risks vs. payoffs they carry. In short, they suggest that when encountering a new and potentially dangerous scenario, the best strategy may be to simply march in with the assumption that you’re going to win, until you’re proven wrong.

As the journal Nature reports, the University of Edinburgh’s Dominic D. P. Johnson and UCSD’s James H. Fowler tested this concept by constructing a mathematical model of simplified resource competition, in which pairs of individuals endowed with different competitive strategies battle it out over limited resources:

If neither individual claims [a] resource, then no fitness is gained. If only one individual makes a claim, then it acquires the resource and gains fitness and the other individual gains nothing. If both individuals claim the resource, then both individuals pay a cost due to the conflict between them, but the individual with the higher initial endowment will win the conflict and also obtain fitness for acquiring [the resource].

In other words, conflict creates cost, but that may be a risk worth taking, because the payoff for a win is so high.

Intriguingly, the researchers found that the usefulness of overconfidence depends on how many resources are around, compared with how high the cost of competition is:

Overconfidence maximizes individual fitness and populations tend to become overconfident, as long as benefits from contested resources are sufficiently large compared with the cost of competition. In contrast, unbiased strategies are only stable under limited conditions.

This makes sense from an evolutionary perspective, the researchers say, because overconfident animals – if they live long enough to produce offspring – may be more likely to have lots of children; and they’re also likely to end up with an overabundance of resources to help ensure those children’s survival.

Though this is all quite a bit of a leap from the actual data, it does provide an interesting perspective on conquerors like Genghis Khan, whose living descendants number in the millions. Clearly, from an evolutionary perspective, the guy was doing something right.

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1. This famous quote, from the Roman historian Pliny the Elder, actually has another layer of meaning – in Latin, the phrase is “Fortes Fortuna adiuvat,” and it literally means that Fortuna, the goddess of luck, helps and supports brave people when they leap into action. So, as unscientific as it may be, it’s still kinda cool to think that when you take risks, a goddess is flying to your aid. Then again, Pliny supposedly said these words right before sailing toward the erupting Mount Vesuvius and suffocating to death on poisonous fumes – so, you know, there’s that.

Generosity Psychology

New research explains why it makes evolutionary (and mathematical) sense for us to be kind to strangers.

"It makes evolutionary sense for me to never let go of you...ever!"

The study, published in the Proceedings of the National Academy of Sciences, shows that people are, on average, more generous to strangers than most mathematical models predict – and that there’s a logical reason for cooperation to evolve this way: it often doesn’t cost much to be generous, but a single act of stinginess could cost you a long-term friend. In other words, petty greed just isn’t worth the risk.

This conclusion might seem face-slappingly obvious, but what’s intriguing here is the fact that it has a solid mathematical basis. A team led by psychologists Andrew Delton and Max Krasnow of the University of California, Santa Barbara constructed computer simulations of natural selection systems.

The “agents” (i.e., simulated individuals) used a Bayesian reasoning process to predict whether they would interact with the same partner in the future, and factored this information into their decisions about whether or not to be generous in a Prisoner’s Dilemma-type game. As it turned out, though, cooperation was a more evolutionarily stable strategy whether or not an agent reasoned that it would encounter the same partner again:

Even though their beliefs were as accurate as possible, our simulated people evolved to the point where they essentially ignored their beliefs and cooperated with others regardless. This happens even when almost 90 percent of the interactions in their social world are actually one-time rather than indefinitely continued.

This is in stark contrast to loads of previous mathematical models, which predicted that the best strategy is to be generous with one’s regular reciprocal partners, but selfish in one-time-only interactions. Instead, this research shows that the cost/benefit ratio for both these kinds of generosity is about the same:

The conditions that promote the evolution of reciprocity — numerous repeat interactions and high-benefit exchanges — tend to promote one-shot generosity as well. Consequently, one-shot generosity should commonly coevolve with reciprocity.

It’s also interesting to note that this model predicts the same sort of generosity regardless of the size of the group – what’s important isn’t how likely you are to meet the same person again, but simply that there is a chance, however slight, that they might help you in the future.

This research caught my eye because of something that happened to me the other night: my friend and I were eating at a restaurant, when we noticed the people at the next table over loudly lecturing the waitress – scolding her, even – over the allegedly poor quality of the food. They refused to pay, and finally stormed out of the place. When my friend and I asked the waitress what had happened, she rehashed the customers’ complaints for us, then mentioned that almost every other table in the restaurant had called her over to offer stern judgments of the rude customers, and supportive words for her (both of which we also did).

As this research demonstrates, it was more than just empathy or an ancestral tribe mentality that influenced our actions that night – though those factors did have their roles, and might be reflections of a more underlying mathematical truth (as so many patterns in nature are). But odds are, neither we nor the rude customers will ever see that waitress again – and being kind to her only gained us a few moments of positive feelings. Nevertheless, being nice to that harmless stranger “felt right” to us – and as it happens, there’s an evolutionary reason for that.

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