Abstract

The problem of a priori estimation of the result of a mulicriteria two-person competitive game is considered in the framework of operations research. Various aspects of decision making in such games are discussed. Relations between the values of a vector best guaranteed result (BGR) for both players are obtained. The difference of the mulicriteria antagonistic game considered as a model of taking into account the natural uncertainty from the mulicriteria zero-sum game considered as interaction with a purposeful opponent is formalized. Special attention is paid to the concepts of the value and solution of the latter game. As the basic solution of this game, we use the multicriteria Shapley equilibrium when it gives to each player the result not worse than her or his BGR. It is shown that the last condition is not restrictive. The definition of the one-sided value of the multicriteria game as the player’s BGR if her BGR is independent of the order of the players' moves and the definition of the corresponding one-sided solution are given. It is proved that the equilibrium is weaker than the one-sided solution, and the equilibrium always exists in mixed strategies. The existence of a one-sided solution in mixed strategies is guaranteed by a special interpretation of multicriteria averaging. To justify the conclusions, Slater’s value of the multicriteria optimum is parameterized using Germeier’s scalarizing function.

中文翻译：

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多准则竞争博弈作为运筹学模型

摘要

在运筹学的框架内考虑了先验估计两人竞争性博弈游戏结果的问题。讨论了此类游戏中决策的各个方面。获得两个参与者的向量最佳保证结果（BGR）的值之间的关系。形式多样的对抗性对抗游戏的差异被正式考虑为模型，该模型考虑了来自对抗性零和博弈的自然不确定性，后者被认为是与有目的的对手互动。要特别注意后一种游戏的价值和解决方案的概念。作为该游戏的基本解决方案，我们使用多准则Shapley平衡法，即它给每个玩家带来的结果都不会比她或他的BGR差。结果表明，最后一个条件不是限制性的。如果多准则游戏的单边价值独立于玩家移动的顺序，则将多准则游戏的单边价值定义为玩家的BGR，并给出相应的单边解的定义。证明了均衡比单边解弱，并且均衡总是存在于混合策略中。混合策略中单边解决方案的存在通过对多准则平均的特殊解释来保证。为了证明结论的正确性，使用Germeier的标量函数对多标准最优的Slater值进行参数化。证明了均衡比单边解弱，并且均衡总是存在于混合策略中。混合策略中单方面解决方案的存在通过对多准则平均的特殊解释来保证。为了证明结论的正确性，使用Germeier的标量函数对多标准最优的Slater值进行参数化。证明了均衡比单边解弱，并且均衡总是存在于混合策略中。混合策略中单边解决方案的存在通过对多准则平均的特殊解释来保证。为了证明结论的正确性，使用Germeier的标量函数对多标准最优的Slater值进行参数化。