| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
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| Research Abstract |
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.
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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
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