A Perturbation on Two-Person Zero-Sum Games
A Perturbation on Two-Person Zero-Sum Games
复制标题
二人零和博弈的扰动
DOI：
10.1007/978-1-4612-1336-9_15
复制
发表时间：
2000
期刊：
影响因子：
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通讯作者：
Kensuke Tanaka
中科院分区：
文献类型：
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作者：
Y. Kimura;Yoichi Sawasaki;Kensuke Tanaka
在本文中，我们研究了受约束函数扰动的两人零和博弈。我们需要在各种条件下证明博弈存在鞍点。但是，在许多情况下，直接搜索鞍点似乎很困难。如果扰动博弈存在 amax-inf(ormini-sup)，则该博弈具有鞍点，那么在某些条件下，玩家 I（或玩家 II）对于修改后的扰动博弈具有弱最优解，其共轭损失函数由下面的连续仿射函数的上包络变换而来。此外，如果原始博弈的损失函数是凸且下半连续的，则利用其双共轭损失函数，我们证明原始扰动博弈具有鞍点。
In this paper, we investigate a two-person zero-sum game perturbed by constrained functions. We need, under the various conditions, to show that there exists a saddle point for the game. But, in many cases, it seems to be difficult to search directly for a saddle point. If there exists amax-inf(ormini-sup) of the perturbed game, the game has asaddle valueand then, under some conditions, Player I (or Player II) has a weak optimal solution for the modified perturbed game with conjugate loss functions transformed by the upper envelope of the continuous affine functions from below.Moreover, if loss functions of the original game are convex and lower semicontinuous, using its biconjugete loss functions, we show that the original perturbed game has a saddle point.
DOI：
10.2307/3323470
发表时间：
1985-01
期刊：
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影响因子：
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作者：
Willi Hock;K. Schittkowski
通讯作者：
Willi Hock;K. Schittkowski