Game Theory and Statistical Mechanics.

研究人员将在博弈论、统计力学和概率论的交叉点上开展几个项目。其中一系列项目围绕博弈论和统计力学之间的深层联系展开，这些联系在很大程度上尚未被探索。一方面，博弈论的概念极大地丰富了统计力学的建模工具，另一方面，非平衡统计力学的最新进展给博弈论带来了新的曙光。特别是，研究人员将研究某些零和博弈与不可逆性和熵产生的概念之间的联系。另一系列项目涉及通过随机过程、确定性方程和进化博弈中的随机-确定性混合模型来开发多尺度模型。需要这些工具来模拟具有多个时空尺度的复杂系统，例如电信网络中灵活的实时频率交易或争夺空间分布客户的公司之间的垄断竞争。研究人员将与数学家、经济学家和计算机科学家合作，目标是开发足够的数学工具并构建现实的模型。以冯·诺伊曼、纳什和其他许多人为起点的博弈论一直是、现在仍然是数理经济学的重要工具。演化博弈论始于20世纪80年代初的S，特别是生物学家梅纳德-史密斯，它将传统的静态战略均衡概念与学习机制的实施和通过动态机制进行的战略传递相结合。进化游戏现在在人口生物学、社会科学、计算机科学以及物理学中得到了显著的应用。研究人员的工作一方面是受到博弈论和物理学(特别是非平衡统计力学)之间深刻的理论联系的推动。另一方面，研究人员还致力于开发数学工具，结合博弈论和概率论对复杂的多尺度问题进行建模。一个值得注意的挑战是构建一个基于代理的移动通信网络频谱交易模型。由于移动通信设备的爆炸性发展，预计在不久的将来，这类问题将变得至关重要。

The investigator will be working on several projects at the intersection of game theory, statistical mechanics, and probability. One series of projects is centered around the deep and largely unexplored connections between game theory and statistical mechanics. On one hand, game theoretical concepts enrich greatly the modelling tools of statistical mechanics and, on the other hand, recent advances in non-equilibrium statistical mechanics shed a new light on game theory. In particular the investigator will work on the connections between certain zero-sum games and the concepts of irreversibility and entropy production. Another series of projects involve the development of multiscale modelling via stochastic processes, deterministic equations, and hybrid stochastic-deterministic models in evolutionary games. These tools are needed to model complex systems with multiple spatio-temporal scales such as flexible real-time frequency trading in telecommunication networks or monopolistic competitions between companies vying for spatially distributed customers. The investigator will work in collaboration with mathematicians, economists and computer scientists with the goals to develop adequate mathematical tools and to construct realistic models. Game theory starting with Von Neumann, Nash, and many others has always been, and still is, a crucial tool in mathematical economics. Starting in the early 1980's, in particular due to the biologist Maynard-Smith, evolutionary game theory was born and it combines the traditional static concepts of strategic equilibria with the implementation of learning mechanisms and strategy transmissions via dynamical mechanisms. Evolutionary games are now used notably, in population biology, social sciences, computer sciences, as well as physics. The investigator's work is motivated on one hand by the deep theoretical connections between game theory and physics (in particular non-equilibrium statistical mechanics). On the other hand the investigator also aims to develop the mathematical tools to model complex multiscale problems with a combination of game theory and probability. A notable challenge is to construct an agent-based model for spectrum trading in mobile telecommunication networks. Problems of this type are expected to be crucially important in the near future due to the explosive development of mobile telecommunication devices.