Applications of differential games to trade theory

微分博弈在贸易理论中的应用

• 批准号: 07630014
• 负责人: SHIMOMURA Kazuo
• 金额: $ 0.45万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07630014/
• 关键词: differential game; optimal control theory; feedback-Nash equilibrium; homogeneity in differential equations and felicity functions; multiple state variables; linear Markov strategy; 国際貿易論; 内生的経済成長論; 最適制御理論; 偏微分方程式論; Feedback-Nash解; 均衡解のパラメーターへの

Let us atate the main theorem that was proved in the present project Consider a differential game as follows :(1) The numbers of playrs, state variables and control variables of each playr, say M,N and J_i, i=1, ..., M,are arbitrarily fixed.(2) Let x and c_i are an N-dimensional vector of state variables and an J_<ii>-dimensional vector of control variables of playr i. Let us assume that the motion of x is determined by the system of differential equationsx^^・=F (x, c),where c= (c_1, ...c_M). Let us denote the objective functional of playr i byV_i=*u_i (c_i) exp [-rt] dtwhere the rate of time preference r is assumed to be positive and constant.In this differential game, we can state that :Assume that u_<ii> is homogeneous of degree alpha>0, that F is homogeneous of degree one in x and c, and that all playr i's opponents use Markov strategies that are homogeneous of degree one. Then(ii) Playr i's best reply is homogeneous of degree one in x.(ii) The maximized value function V_i is homogeneous of degree alpha in x.The proof can be found in Long and Shimomura (Journal of Economic Behavior and Organization, December 1997).

本文证明了一个微分对策的主要定理：（1）局中人的数目，每个局中人的状态变量和控制变量，设M，N和J_i，i=1，…，M是任意固定的。(2)设x和c_i分别是参与者i的状态变量的N维向量和<ii>控制变量的J维向量。让我们假设x的运动由微分方程组x ^^·=F（x，c）决定，其中c=（c_1，.. c_M）。设局中人i的目标泛函为V_i=*u_i（c_i）exp [-rt] dt，其中时间偏好率r为正且常数，在此微分对策中，设u_<ii>i为α&gt;0次齐次，F在x和c上均为1次齐次，且所有局中人i的对手均采用1次齐次马尔可夫策略。则（ii）Playr i的最佳对策是x中的一次齐次对策. (ii)最大值函数V_i在x中是α次齐次的。证明可以在Long和Shimomura（Journal of Economic Behavior and Organization，1997年12月）中找到。

项目成果

Shimomura, K.and Tran-Nam, B..: "Education, Human Capital and Economic Growth in an Overlapping Generations Model" Kokumin Keizai Zasshi. 175. 63-79 (1997)

Shimomura, K. 和 Tran-Nam, B..：“代际重叠模型中的教育、人力资本和经济增长”Kokumin Keizai Zasshi。

下村和雄: "“Some Results on the Markov equilibria of a Class of Homogeneous Differential Games"" Journal of Economic Behavior and Organization. 34. (1997)

Kazuo Shimomura：“一类同质微分博弈的马尔可夫均衡的一些结果”，经济行为与组织杂志 34。（1997）。

K.Shimomura: "A Dynamic Equilibrium Model of Durable-Goods Mopnopoly" Journal of Economic Behavior and Organization. 34. (1997)

K.Shimomura：“耐用品垄断垄断的动态均衡模型”经济行为与组织杂志。

下村和雄: "“A Dynamic Equilibrium Model of Durable-Goodx Mopnopoly"" Journal of Economic Behavior and Organization. 34. (1997)

Kazuo Shimomura：“Durable-Goodx Mopnopoly 的动态均衡模型”，经济行为与组织杂志 34。（1997 年）

下村和雄: "“Education, Human Capital and Economic Growth in an Overlapping Generations Model"" 国民経済雑誌. 175. 63-79 (1997)

下村一夫：“代际重叠模型中的教育、人力资本和经济增长””国民经济杂志 175. 63-79 (1997)