Abstract: This paper considers two-person zero-sum games with continuous strategies and investigates the existence of the equilibrium strategy. First, we examine the two-person zero-sum game with complete information on both sides, demonstrate the existence of the equilibrium strategy and present a method to find it. Further, we study the two-person zero-sum game with incomplete information, namely, the exact payoff function is unknown for both players. Under the assumption that each player thinks of the other as a risk-averse decision maker, we analyze the existence of the equilibrium strategy with regard to the incomplete information game, and develop an approach to find an equilibrium point when it exists. Finally, a numerical illustration is given to verify the feasibility of the proposed methods.

Key words: continuous strategy, two-person zero-sum games, equilibrium strategy, incomplete information

摘要： 考虑连续区间策略下的二人零和对策问题,研究其均衡策略的存在性。首先分析了完全信息下的二人零和对策问题,证明了该问题均衡策略的存在性并给出求解方法。然后进一步研究了收益函数不确定的不完全信息二人零和对策问题,在各局中人都认为对方是风险厌恶型的假设下,分析该类对策纯策略均衡的存在性,并通过研究纯策略均衡存在的充要条件给出判断并寻找纯策略均衡解的方法。最后给出一个数值算例,验证本文所提出方法的可行性。

关键词: 连续区间策略, 二人零和对策, 均衡策略, 不完全信息