有限理性条件下演化博弈行为分析

基于博弈双方有限理性的假设,运用动力系统的相关理论和方法对一般2×2非对称演化博弈过程建立了动态复制方程,并对博弈双方在演化过程中的行为进行了分析,得出博弈双方交互系统均衡点及稳定性相应的结论及其全部动力学行为.     

A lemma in open sequential voting by veto

The paper is devoted to the investigation of intuitively rational choice in a hierarchical game that is a model of election by open sequential veto-voting. Casting a veto against voter’s least preferred alternative (among remaining ones) may not lead to a sophisticated equilibrium. It means that sincere choice (being intuitive) is not rational. There arises the problem of finding conditions under which a sophisticated optimal sequence of actions is intuitively rational. We prove that in the case of strict preference ordering of alternatives, there exists an intuitively rational sophisticated optimal sequence. In the sequence, each voter vetoes an alternative less preferred than the sophisticated equilibrium outcome. Thus, only intuitively rational strategies are to be considered, although complete information about voters’ preferences is still needed.     

考虑居民选择行为的应急避难场所选址问题研究

突发事件发生后,应急管理部门将面临选择启用哪些应急避难场所供居民避难的决策。与其它设施选址不同,处于有限理性状态下的居民可选择是否去避难以及去哪个避难所避难。为使未被服务的居民数量最小化,考虑居民的有限理性选择行为至关重要。为此,考虑居民避难距离及避难所吸引力等因素,基于竞争选址理论构建避难所对居民的效用函数。在此基础上,运用多项logit模型刻画居民的有限理性选择行为,建立基于有限理性选择行为的选址模型,并与基于效用最优选择行为和基于系统最优原则的选址模型进行对比以验证模型的合理性。为了高效地求解模型,设计了模拟退火算法和遗传算法两种启发式算法。算例分析结果验证了模型和算法的可行性和有效性,并揭示了居民理性程度、选址个数及财政预算均对选址结果有重要影响。     

A consumption model with separability and imperfect decision makers

A consumption model is considered, where agents may have a simplified image of reality and a simplified way of reaching decisions. Some rules of behaviour are assumed, considering, in particular, the decision-theoretic ideas of decentralization and price aggregation. The consumers have a price-independent relative income distribution. The existence and unicity of temporary equilibria are investigated.      

Evolutionary dynamics may eliminate all strategies used in correlated equilibrium

We show on a 4×4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown–von Neumann–Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard regularity conditions. For the replicator dynamics and the best-response dynamics, elimination of all strategies used in correlated equilibrium is shown to be robust to the addition of mixed strategies as new pure strategies.     

Study on a 3-dimensional game model with delayed bounded rationality

A nonlinear dynamic triopoly game model is studied based on the theory of nonlinear dynamics and previous researches in this paper. A lagged structure is introduced to the model to study stability conditions of the Nash equilibrium under a local adjustment process when players price their products with delayed bounded rationality. Numerical simulations are provided to demonstrate the complexity of system evolvement and influence of the strategy of delayed bounded rationality on system stability. We find that besides the lagged structure, suitable delayed parameters are also important factors to eliminate chaos or expand the stable region of the system, and various players’ adjustment parameters have different effect on stability of the system.     

The rise of complex phenomena in Cournot duopoly games due to demand functions without inflection points

In this paper, we propose Cournot duopoly games where quantity-setting firms use non-linear demand functions that have no inflection points. Two different kinds of repeated games are introduced based on rationality process of firms and Puu’s incomplete approach. First, a model of two rational firms that are in competition and produce homogenous commodities is introduced. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation and chaos are investigated. By using rationality process firms do not need to solve any optimization problem but they adjust their production based on estimation of the marginal profit. Using Puu’s incomplete information approach a new model is introduced. As in the first model, the equilibrium points are obtained and their dynamical characteristics are investigated. By using Puu’s approach firms only need to know their profits and the quantities produced in the past two times. We compare the properties of the two models under the two approaches. The paper extends and generalizes the results of other authors that consider similar processes.     

关于Nielson Zeta函数的有理性

Ａ．Ｌ．Ｆｅｌ＇ｓｈｔｙｎ和Ｖ．Ｂ．Ｐｉｌｙｕｇｉｎａ定义了Ｎｉｅｌｓｏｎｚｅｔａ函数并证明关于其有理性的一些结果，本文改进了他们的一些结果。     

指派问题的多重最优解的择优方法

在某些情况下,经典指派问题的最优解不唯一．不同的最优解对参与人的影响不同,导致每个参与人会争取最有利于自身的最优解．为解决这个问题,通过研究允许合作指派问题的合作对策解的形成,提出允许合作指派问题的讨价还价模型和个体理性激励函数．在此基础上,提出了一个考虑个体理性的指派问题多重最优解的择优方法,从而保证了指派问题最优解的唯一性．