Evolutionary dynamics of populations with conflicting interactions: Classification and analytical treatment considering asymmetry and power
Evolutionary dynamics of populations with conflicting interactions: Classification and analytical treatment considering asymmetry and power
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DOI：
10.1103/physreve.81.016112
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发表时间：
2010-01-01
影响因子：
2.4
通讯作者：
Johansson, Anders
中科院分区：
文献类型：
--
作者：
Helbing, Dirk;Johansson, Anders
进化博弈论已经被成功地用于研究系统的动力学，在这个系统中，许多实体具有竞争性的相互作用。从物理学的角度来看，研究相互作用的实体发生协调或合作的条件是很有趣的，无论是自旋、粒子、细菌、动物还是人类。在这里，我们分析了实体是异质的情况，特别是两个种群具有冲突的交互和两个可能的状态的情况。对于这样的系统，将为定常解和相关的特征值确定明确的数学公式，这决定了它们的稳定性。这样，就可以对四种不同类型的系统动力学进行分类，并讨论它们之间的各种相变。虽然这些结果从物理学的角度来看很有趣，但它们也与社会、经济和生物系统相关，因为它们允许人们理解以下条件：(1)合作的破裂，(2)不同行为的共存(“亚文化”)，(3)共同行为的演变(“规范”)，以及(4)两极分化或冲突的发生。我们指出，规范在社会系统中的作用类似于力在物理学中的作用。
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur, be it spins, particles, bacteria, animals, or humans. Here, we analyze the case, where the entities are heterogeneous, particularly the case of two populations with conflicting interactions and two possible states. For such systems, explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues, which determine their stability. In this way, four different types of system dynamics can be classified and the various kinds of phase transitions between them will be discussed. While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors ("subcultures"), (3) the evolution of commonly shared behaviors ("norms"), and (4) the occurrence of polarization or conflict. We point out that norms have a similar function in social systems that forces have in physics.