网上平衡对策与流向对策值的存在性

THE EXISTENCE OF VALUES OF BALANCED GAME AND GAME OF FLOW ON THE NETWORK

在一个网络上可以赋以流量，网上每一个孤可以与一个Ｎ人对策的局中人相对应，有了这种对应之后，我们证明了任何一个可加性对策都是流向对策，且证明了如果Ｖ１，Ｖ２是流向对策，则ｍｉｍ｛Ｖ１，Ｖ２｝也是流向对策．在此基础上，我们证明了θ－全平衡对策是流向对策这一主要定理．最后，我们成功地构造了一个很简单的例子说明了此定理的逆命题不成立．这是其它文献［１，２，３，４］中都没有明确指出的结论．关于θ－全平衡对策与流向对策的关系．目前来看我们的结果是较好的结果［９］．

A flow can be bestowed on a network. Each arc on the network can correspond with a player in a n-person game. With this corresponding, we,ve not only proved that an additive game is a flow game,but also proved that min {V1,V2 } is also a flow game if V1 ,V2 are flow games. From these conclusions,we are able to show our main theorem that the θ-totally balanced game is a. flow game. Eventually, we've succeeded in making a very simple example to show that the converse proposition of this theorem is not reasonable. This conclusion can not be found evidently from other works [1,2, 3, 4]. Our conclusion about the relationship between the θ-totally balanced game and the flow game is so far a preferable one [9].