供应链金融信贷市场三方演化博弈动态

供应链金融业务的产生与发展为中小微企业的融资提供了有效的途径。核心企业在为中小微企业提供信用担保的同时,也对中小微企业的生产等经济活动进行监督,以维持供应链上各企业的信用及效益。本文考虑供应链金融各参与方之间的相互影响,构建“金融机构——核心企业——中小微企业”三方博弈主体的演化博弈动态模型。运用演化博弈理论与Lyapunov判别法分析三方演化动态模型的均衡点以及其渐进稳定性。结论表明:中小微企业得到的预期利益越大、违约的成本越大,就越不容易选择违约,供应链金融信贷系统将演化到核心企业为中小微企业提供贷款信用担保,金融机构对中小微企业进行贷款、中小微企业选择不违约的演化均衡状态,信贷市场呈良性发展的趋势。     

具有模糊支付的Moran过程演化博弈动态

以往对演化博弈的研究都假设个体从博弈中获得的支付是确定的并以精确的数来表示。然而由于受环境中各种不确定因素的影响,个体博弈时所获得的支付并不是一个精确的数值,而需要用一个模糊数来表示。本文研究模糊支付下2×2的对称博弈, 利用模糊数的运算, 分析具有模糊支付的有限种群Moran过程演化动态。在弱选择下以梯形模糊数和三角模糊数表示博弈支付,计算策略的模糊扎根概率,分析自然选择有利于策略扎根及策略成为模糊演化稳定策略的条件。将经典博弈推广到模糊环境中丰富了演化博弈理论,更具有现实意义。     

Feedback arcs and node hierarchy in directed networks

Directed networks such as gene regulation networks and neural networks are connected by arcs(directed links). The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which leads to complex information-processing dynamics in the network and makes it highly challenging to infer the intrinsic direction of information flow. In this theoretical paper, based on the principle of minimum-feedback, we explore the node hierarchy of directed networks and distinguish feedforward and feedback arcs. Nearly optimal node hierarchy solutions, which minimize the number of feedback arcs from lower-level nodes to higher-level nodes, are constructed by belief-propagation and simulated-annealing methods. For real-world networks, we quantify the extent of feedback scarcity by comparison with the ensemble of direction-randomized networks and identify the most important feedback arcs. Our methods are also useful for visualizing directed networks.     

Statistical physics of hard combinatorial optimization:Vertex cover problem

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics,and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity.In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial(NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.