Washington, May 29: Have you ever wondered why do people make anonymous donations, and why does the public perceive this as admirable? Or why do some of us like to risk our lives to save an animal from the potential danger? A team of researchers decided to explore the possibilities and came up with the interesting logic behind modesty and humbleness.

According to a study led by the Institute of Science and Technology Austria, modesty can evolve naturally. The set of researchers developed a novel game-theoretic model that captured these behaviours and enabled their study. Their new model was the first to include the idea that hidden signals, when discovered, provide additional information about the sender. They used this idea to explain under which circumstances people have an incentive to hide their positive attributes.

People often take actions that may be costly at first, but lead to reputational benefits in the long run. However, if good reputations are important, why are there numerous situations in which people hide accomplishments or good characteristics, like when we donate anonymously? Similarly, we often emphasise subtlety in art or fashion, avoid appearing over-eager, or otherwise obscure something positive. Why do others consider this behaviour commendable? The team's key insight into this societal puzzle is that 'burying' a signal (i.e. obscuring information) is a signal in and of itself.

This additional signal can have several interpretations: for instance, the sender may be unconcerned with those who might have been impressed, but who miss subtle messages (like an artist disregarding the philistine masses). Alternatively, the sender might be confident that those who matter to them will find out anyway (for instance, only those who have the taste and/or necessary wealth will recognise a designer bag without an obvious logo).

The scientists succeeded in formalising these ideas in a new evolutionary game theory model they call the 'signal-burying game'. In this game, there were different types of senders (high, medium, and low), and different types of receivers (selective and unselective). The sender and the receiver did not know the other's type. To convey their type, senders had to pay a cost to send a signal. Signals could be sent clearly or be buried. When a signal was buried, it had a lower probability of being observed by any kind of receiver.

In particular, buried signals entailed the risk that receivers would never learn that the sender has sent a signal at all. After the sender had made his signalling decision, receivers decided whether or not to engage in an economic interaction with the sender. The game had an element of risk, and therefore, senders and receivers were required to develop strategies to maximise their payoff.

"We wanted to understand what strategies would evolve naturally and be stable," explained Christian Hilbe, co-first author of the study. "In particular, is it possible to have a situation where high-level senders always choose to bury their signals, mid-level senders always send a clear signal, and low-level senders send no signal at all?"

This would correspond to situations that come up in real life, and is one of the key distinguishing features of their model: they allow for strategies that target specific receivers at the risk of losing others. In their simulations, players started off neither sending nor receiving signals. Then, with some probability, a player either selected a random strategy (representing mutation) or imitated another player (representing a learning process biased towards strategies with higher payoff). In their simulations, the scientists found that populations quickly settled at the strategy described above.

The team also developed several extensions to the model, enabling them to cover more general scenarios. First, they added different levels of obscurity: senders could choose from several revelation probabilities. "We found that in this case, high senders tend to be modest...but not too modest," added Hilbe. "Even if you're humble, you don't try to be holier-than-thou." It was moreover possible to increase the number of types of senders and receivers, as well as introduce subtleties in the preferences of the receivers.

Using their new model, Hilbe and team were able to put a different perspective on various common situations: a donor giving anonymously, an academic not disclosing their degree, an artist creating art with hidden messages, and a possible partner hiding their interest, among others. Evolutionary game theory showed that, in the end, these puzzling social behaviours make sense. The study is published in the journal Nature Human Behaviour.