Helbing Dirk, Johansson Anders
CLU, ETH Zurich, CLU E 1, Zurich, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jan;81(1 Pt 2):016112. doi: 10.1103/PhysRevE.81.016112. Epub 2010 Jan 26.
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.
进化博弈论已成功用于研究许多实体存在竞争相互作用的系统动力学。从物理学角度来看，研究相互作用的实体在何种条件下会出现协调或合作是很有意思的，这些实体可以是自旋、粒子、细菌、动物或人类。在此，我们分析实体为异质的情况，特别是具有冲突相互作用且有两种可能状态的两个种群的情况。对于此类系统，将确定平稳解和相关特征值的显式数学公式，这些公式决定了它们的稳定性。通过这种方式，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。虽然从物理学角度来看这些结果很有意思，但它们对社会、经济和生物系统也很重要，因为它们能让人理解以下几种情况的条件：（1）合作的瓦解；（2）不同行为（“亚文化”）的共存；（3）共同行为（“规范”）的演变；（4）两极分化或冲突的出现。我们指出，规范在社会系统中具有与物理学中的力类似的功能。
