John Maynard Smith and evolutionary game theory

The early rise and spread of evolutionary game theory: perspectives based on recollections of early workers

Though the first attempts to introduce game theory into evolutionary biology failed, new formalism by Maynard Smith and Price in 1973 had almost instant success. We use information supplied by early workers to analyse how and why evolutionary game theory (EGT) spread so rapidly in its earliest years. EGT was a major tool for the rapidly expanding discipline of behavioural ecology in the 1970s; each catalysed the other. The first models were applied to animal contests, and early workers sought to improve their biological reality to compare predictions with observations. Furthermore, it was quickly realized that EGT provided a general evolutionary modelling method; not only was it swiftly applied to diverse phenotypic adaptations in evolutionary biology, it also attracted researchers from other disciplines such as mathematics and economics, for which game theory was first devised. Lastly, we pay attention to exchanges with population geneticists, considering tensions between the two modelling methods, as well as efforts to bring them closer. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Heterogeneous update mechanisms in evolutionary games: Mixing innovative and imitative dynamics

Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows the introduction of elements of novelty, while the latter is responsible for the motion of a system in its phase space. Often, these processes are strongly related, since an innovation can trigger the evolution, and the latter can provide the optimal conditions for the emergence of innovations. Both processes can be studied by using the framework of evolutionary game theory, where evolution constitutes an intrinsic mechanism. At the same time, the concept of innovation requires an opportune mathematical representation. Notably, innovation can be modeled as a strategy, or it can constitute the underlying mechanism that allows agents to change strategy. Here, we analyze the second case, investigating the behavior of a heterogeneous population, composed of imitative and innovative agents. Imitative agents change strategy only by imitating that of their neighbors, whereas innovative ones change strategy without the need for a copying source. The proposed model is analyzed by means of analytical calculations and numerical simulations in different topologies. Remarkably, results indicate that the mixing of mechanisms can be detrimental to cooperation near phase transitions. In those regions, the spatial reciprocity from imitative mechanisms is destroyed by innovative agents, leading to the downfall of cooperation. Our investigation sheds some light on the complex dynamics emerging from the heterogeneity of strategy revision methods, highlighting the role of innovation in evolutionary games.