Animal acoustic communication contains many structural features. Among these, temporal structure, or rhythmicity, is increasingly tested empirically and modelled quantitatively. Accelerando is a rhythmic structure which consists of temporal intervals increasing in rate over a sequence. Why this particular vocal behaviour is widespread in many different animal lineages, and how it evolved, is so far unknown. Here, we use evolutionary game theory and computer simulations to link two rhythmic aspects of animal communication, acceleration and overlap: We test whether rhythmic accelerando could evolve under a pressure for acoustic overlap in time. Our models show that higher acceleration values result in a higher payoff, driven by the higher relative overlap between sequences. The addition of a cost to the payoff matrix models a physiological disadvantage to high acceleration rates and introduces a divergence between an individual's incentive and the overall payoff of the population. Analysis of the invasion dynamics of acceleration strategies shows a stable, non-invadable range of strategies for moderate acceleration levels. Our computational simulations confirm these results: A simple selective pressure to maximise the expected overlap, while minimising the associated physiological cost, causes an initially isochronous population to evolve towards producing increasingly accelerating sequences until a population-wide equilibrium of rhythmic accelerando is reached. These results are robust to a broad range of parameter values. Overall, our analyses show that if overlap is beneficial, emergent evolutionary dynamics allow a population to gradually start producing accelerating sequences and reach a stable state of moderate acceleration. Finally, our modelling results closely match empirical data recorded from an avian species showing rhythmic accelerando, the African penguin. This shows the productive interplay between theoretical and empirical biology.

Evolutionary game theory focuses on the fitness differences between simple discrete or probabilistic strategies to explain the evolution of particular decision-making behavior within strategic situations. Although this approach has provided substantial insights into the presence of fairness or generosity in gift-giving games, it does not fully resolve the question of which cognitive mechanisms are required to produce the choices observed in experiments. One such mechanism that humans have acquired, is the capacity to anticipate. Prior work showed that forward-looking behavior, using a recurrent neural network to model the cognitive mechanism, are essential to produce the actions of human participants in behavioral experiments. In this paper, we evaluate whether this conclusion extends also to gift-giving games, more concretely, to a game that combines the dictator game with a partner selection process. The recurrent neural network model used here for dictators, allows them to reason about a best response to past actions of the receivers (reactive model) or to decide which action will lead to a more successful outcome in the future (anticipatory model). We show for both models the decision dynamics while training, as well as the average behavior. We find that the anticipatory model is the only one capable of accounting for changes in the context of the game, a behavior also observed in experiments, expanding previous conclusions to this more sophisticated game.

Various social situations entail a collective risk. A well-known example is climate change, wherein the risk of a future environmental disaster clashes with the immediate economic interest of developed and developing countries. The collective-risk game operationalizes this kind of situations. The decision process of the participants is determined by how good they are in evaluating the probability of future risk as well as their ability to anticipate the actions of the opponents. Anticipatory behavior contrasts with the reactive theories often used to analyze social dilemmas. Our initial work can already show that anticipative agents are a better model to human behavior than reactive ones. All the agents we studied used a recurrent neural network, however, only the ones that used it to predict future outcomes (anticipative agents) were able to account for changes in the context of games, a behavior also observed in experiments with humans. This extended abstract aims to explain how we wish to investigate anticipation within the context of the collective-risk game and the relevance these results may have for the field of hybrid socio-technical systems.