Departamento de Física, Universidade Federal do Rio Grande do Sul-RS, Brazil.
School of Computing, University of Kent, Chatham Maritime, United Kingdom.
Phys Rev E. 2018 Apr;97(4-1):042305. doi: 10.1103/PhysRevE.97.042305.
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.
创新和进化是社会和生物系统中两个至关重要的过程。一般来说，前者允许引入新颖元素，而后者则负责系统在相空间中的运动。通常，这两个过程是紧密相关的，因为一个创新可以引发进化，而进化又可以为创新的出现提供最佳条件。这两个过程都可以用进化博弈论的框架来研究，其中进化是一个内在机制。同时，创新的概念需要一个适当的数学表示。值得注意的是，创新可以被建模为一种策略，也可以构成允许代理人改变策略的基本机制。在这里，我们分析了第二种情况，研究了由模仿者和创新者组成的异质群体的行为。模仿者只能通过模仿邻居的策略来改变策略，而创新者则无需复制源就可以改变策略。通过在不同拓扑结构中的分析计算和数值模拟来分析所提出的模型。值得注意的是，结果表明，机制的混合可能对相变附近的合作有害。在这些区域，模仿机制的空间互惠性被创新者破坏，导致合作崩溃。我们的研究揭示了策略修正方法的异质性所产生的复杂动态，突出了创新在进化博弈中的作用。
