An Economic Analysis for Social Conflict using Differential Games

本研究的目的是利用差分博弈分析社会冲突。我们假设一个社会中的每个成员在无限视界上决定他或她的跨期行为，并采取社会中其他成员的行为。我们得到了以下结果：(1)我们的分析侧重于马尔可夫策略，而不是更一般的历史依赖策略，以避免分析的可处理性。(2)在前人关于微分对策的文献中，目标被假设为二次型，线性策略被推导为最优策略。尽管如此，我们认为，除了分析上的便利，没有令人信服的经济理由来限制线性策略。鉴于此，我们关注更一般的非线性马尔可夫策略。这种分析扩展允许每个玩家采取更灵活和理想的策略。此外，由于在我们的分析中，每个参与者的目标函数不是二次的，线性策略可能不存在。通过将策略空间扩展到非线性马尔可夫策略，我们可以避免这种最优策略不存在的情况。(3)Hirshleifer（1991,1995）和Skaperdas（1992）假设了一种无政府状态，其中每个参与者都可以剥夺其他人的资产或产出，而自利和理性的参与者拥有自己的资源，这些资源不受掠夺性活动的支配，并且必须在掠夺性活动和生产活动之间分配这些资源。他们构建了一个静态的单次博弈，并表明在纳什均衡中既不会发生完全冲突，也不会发生完全和平的致敬，并且存在一个部分和平的情况，即每个参与者同时在和平和掠夺性活动之间分配他或她的资源（我们称之为部分和平的情况）。在我们的微分对策中，全局非线性马尔可夫完美均衡策略在长期内导致相同的部分和平局面。(4)我们得到了如下的比较统计结果：无论是掠夺性活动生产率的增加，还是参与人数量的增加，都会使均衡路径偏离帕累托最优路径。相比之下，普通耐用品折旧率的增加或当每个成员都有更长的视野时，均衡路径更接近帕累托最优路径。少

The purpose of this research is to analyze social conflict using differential game. We suppose that each member in a society determines his or her intertemporal behavior over an infinite horizon taking the behabiorof other members in a society. We obtain the following results:(1)Our analysis focus on Markov strategy rather than more general historical dependent strategy in order to avoid the analysis tractable.(2)In the previous literature on differential games the objectives are assumed to be of quadratic form, linear strategies have been derived as an optimal strategy. Nevertheless, we believe that there is no compelling and economic reasons to limit linear strategies except for analytical convenience. In view of this, we focus on more general non-linear Markov strategies. This analytical extension allows each player to take more flexible and desirable strategies. Moreover, since in our analysis the objective function of each player is not quadratic, linear strategies may not exist. … More By extending the strategy space to non- linear Markov strategies, we can avoid such a non-existence of optimal strategies.(3)Hirshleifer (1991,1995) and Skaperdas(1992) have assumed a hypothetical anarchic situation where every player can deprive of other people's asset or output produced and that self-interested and rational players posses their own resources which are not subject to predatory activity and have to allocate those resources between predatory and productive activities. They construct a static one-shot game and show that in a Nash equilibrium neither full conflict not full peaceful salutations occur, and there exist a partial peaceful situation where each player allocate his or her resource between peaceful and predatory activities at the same time (we call a partial peaceful situation). In our differential game globally non-linear Markov perfect equilibrium strategies lead to the same partial peaceful situation in a long run.(4)We have obtained the following comparative statics results: An increase in either the productivity in predatory activity or the number of players makes the equilibrium paths depart from the Pareto optimum one. In contrast, an increase in the depreciation rate of common durable goods or when each member has a longer sight makes the equilibrium path closer to the Pareto optimum one. Less