"The evolution of boundedly rational learning in games"Couto, MartaSocial behavior is often modeled using the mathematical framework of game theory. In its classical form, game theory presumes that individuals are perfectly rational: they know the game's incentive structure and can always compute optimal strategies. Differently, in evolutionary game theory, players do not need to adopt optimal strategies from the outset. However, a usually fixed parameter – selection strength – regulates how often individuals select strategies that might provide higher payoffs. In this sense, we can interpret selection strength as rationality. While rationality has an important role in strategic decision-making, its origins are hardly discussed. If higher rationality allows individuals to better discriminate high-payoff strategies, one would expect that it has an evolutionary advantage. However, in situations where the collective and personal optimal outcomes do not coincide, it is unclear whether full rationality will constantly evolve. As such, we investigate the evolution of rationality for several social dilemmas. We assume individuals interact with each other and learn their strategies by repeatedly assessing payoffs. Importantly, each individual can follow a more or less rational learning rule. At a much slower time scale than the learning process, rationality evolves. Here, we use the adaptive dynamics framework, assuming rationality is a continuous trait. We show that the evolutionary endpoint depends on the game at play. For most prisoner’s dilemmas, rationality evolves towards an ever-increasing value. Surprisingly, however, we find that in prisoner’s dilemmas for which the temptation to defect is small compared to the benefit of mutual cooperation, the evolutionary endpoint is a finite value. We observe a similar result for the majority of the snowdrift games. Differently, for some stag-hunt games, we find evolutionary branching. In summary, we show that full rationality does not always evolve. Notably, this result does not depend on the assumption that higher rationality requires higher cognitive costs. In some scenarios, a seemingly erratic behavior can be strategically justified. These results resonate with earlier ideas and observations in economics and psychology that humans have evolved bounded rationality. Additionally, we shed light on how evolution shapes learning mechanisms for strategic behavior. |
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