https://phys.org/news/2018-05-logic-modestywhy-humble.html

The scientists succeeded in formalizing these ideas in a new evolutionary game theory model they call the "signal-burying game," which they detail in a paper published today in Nature Human Behaviour. In this game, there are different types of senders (high, medium, and low), and different types of receivers (selective and unselective). The sender and the receiver do not know the other's type. To convey their type, senders may pay a cost to send a signal. Signals may be sent clearly or be buried. When a signal is buried, it has a lower probability of being observed by any kind of receiver. In particular, buried signals entail the risk that receivers will never learn that the sender has sent a signal at all. After the sender has made his signaling decision, receivers decide whether or not to engage in an economic interaction with the sender. The game has an element of risk, and therefore, senders and receivers must develop strategies to maximize their payoff.

"We wanted to understand what strategies would evolve naturally and be stable," explains Christian Hilbe, co-first author of the paper and postdoc in the research group of Krishnendu Chatterjee at IST Austria. "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 selects a random strategy (representing mutation) or imitates 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.