Department of Physics, University of Michigan, Ann Arbor, Michigan, United States of America ; Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan, United States of America.
PLoS One. 2013 Sep 10;8(9):e71828. doi: 10.1371/journal.pone.0071828. eCollection 2013.
Co-adaptation (or co-evolution), the parallel feedback process by which agents continuously adapt to the changes induced by the adaptive actions of other agents, is a ubiquitous feature of complex adaptive systems, from eco-systems to economies. We wish to understand which general features of complex systems necessarily follow from the (meta)-dynamics of co-adaptation, and which features depend on the details of particular systems. To begin this project, we present a model of co-adaptation ("The Stigmergy Game") which is designed to be as a priori featureless as possible, in order to help isolate and understand the naked consequences of co-adaptation. In the model, heterogeneous, co-adapting agents, observe, interact with and change the state of an environment. Agents do not, ab initio, directly interact with each other. Agents adapt by choosing among a set of random "strategies," particular to each agent. Each strategy is a complete specification of an agent's actions and payoffs. A priori, all environmental states are equally likely and all strategies have payoffs that sum to zero, so without co-adaptation agents would on average have zero "wealth". Nevertheless, the dynamics of co-adaptation generates a structured environment in which only a subset of environmental states appear with high probability (niches) and in which agents accrue positive wealth. Furthermore, although there are no direct agent-agent interactions, there are induced non-trivial inter-agent interactions mediated by the environment. As a function of the population size and the number of possible environmental states, the system can be in one of three dynamical regions. Implications for a basic understanding of complex adaptive systems are discussed.
共适应（或共同进化），即代理不断适应其他代理自适应行为引起的变化的并行反馈过程，是复杂自适应系统的普遍特征，从生态系统到经济系统。我们希望了解复杂系统的哪些一般特征必然来自共适应的（元）动力学，以及哪些特征取决于特定系统的细节。为了开始这个项目，我们提出了一个共适应模型（“印迹博弈”），其设计目的是尽可能没有先验特征，以便帮助隔离和理解共适应的赤裸裸后果。在该模型中，异质的、共适应的代理观察、相互作用并改变环境的状态。代理不会从一开始就直接相互作用。代理通过在一组随机“策略”中进行选择来适应，这些策略对每个代理都是特定的。每个策略都是代理行为和收益的完整说明。从先验的角度来看，所有的环境状态都是同等可能的，所有的策略收益总和为零，因此如果没有共适应，代理的平均“财富”将为零。然而，共适应的动态产生了一个结构化的环境，只有一部分环境状态以高概率出现（生态位），并且代理积累了正的财富。此外，尽管没有代理之间的直接相互作用，但通过环境存在诱导的非平凡的代理间相互作用。作为种群大小和可能的环境状态数量的函数，系统可以处于三个动态区域之一。讨论了对复杂自适应系统的基本理解的影响。
