混合策略同时博弈I：零和博弈Simultaneous-Move Games with Mixed Strategies I: Zero-Sum Games 第07章
重型机械标准
Chapter 07
混合策略同时博弈
Simultaneous-Move Games with Mixed Strategies
有一类同时博弈是没有纯策略纳什均衡的。
There is a class of simultaneous-move
games that has no Nash equilibria in
pure strategies.
为了预测这些博弈的结果，我们需要扩展关于策略和均衡的概念。
To predict outcomes for such games, we need an extension of our concepts of
strategies and equilibria.
办法是将行动随机化。
This is to be found in the randomization
Slide 3
混合策略同时博弈
Simultaneous-Move Games with Mixed Strategies
随机化行动的要求一般出现在一个博弈者偏爱某种行动组合，而其对手却试图避免他。The need for randomized moves in the play of a game usually arises when one player prefers a coincidence of actions, while her rival prefers to avoid it.零和博弈常常产生类似的直接冲突。Such direct conflict between players arises in zero-sum games.
例如：军事，体育E.g, military conflicts, sporting contests
混合策略同时博弈：一个例子
Simultaneous-Move Games with Mixed Strategies: An Example复配食品添加剂通则
20
90CC 8050DL
社会保险费征缴暂行条例EVERT CC DL
NAVRATILOVA
Slide 5一个混合策略是纯策略的一种随机的混合。A mixed strategy is a random mixture of pure strategies. 在网球博弈中，以概率p 选择DL ，以概率1-p 选择CC ，p 为0到1之间的实数，就是参与者的一个混合策略。In the tennis-point game above, choosing DL with probability p and CC with probability (1-p ) , where p is some real number ranging from 0 to 1, or (p *DL, (1-p )*CC) for short, is a particular mixed strategy available for the player (Evert or Navratilova).这样的混合策略有整个的连续范围，纯策略是其极端情形。There is a whole continuous range of such mixed strategies, including pure strategies as extreme special cases.什么是混合策略？ spss16.0What Is A Mixed Strategy?来自混合策略的收益，就是构成该混合策略的纯策略组合所对应收益的概率加权平均－期望收益。The payoffs from a mixed strategy are defined as the corresponding probab
ility-weighted averages of the payoffs from its constituent pure strategies –expected payoffs.问：面对纳娃的DL ，埃芙特的混合策略(0.75DL, 0.25CC)带给她收益是多少？Q: Against Navratilova ’s DL, what is
Slide 7
纳什均衡就是一组混合策略，其中每一个策略对应一个参与者，满足以下条件：每个人的选择都是她的最优选择，也就是说，给定其他人的混合策略，该选择带给她最高的收益。Nash equilibrium is defined as a list of mixed strategies, one for each player, such that the choice of each is her best choice, in the sense of yielding the highest expected payoff for her, given the mixed strategies of the others.什么是混合策略？
What Is A Mixed Strategy?作为信念和反映的系统，纳什均衡也可以定义为：As a system of beliefs and response, Nash equilibrium can also be define as:
挠脚心论坛每个参与者要形成对其他参与者所出混合策略概率的一个信念，并针对它做出最优反应。Each player forms beliefs about the probability of the mixture that the other is choosing and chooses her own best response to this. 信念正确。就是说，参与者知道、算出或猜出其他参与者从他基于的纯策略中进行选择的正确概率。The beliefs are correct. That is, the player knows, or calculated or guesses th
e correct probabilities with which the other player chooses from among her underlying basic or pure actions.
太原师范学院学报Slide 9
允许博弈中出现混合策略，自动和几乎完全地解决了可能出现的无纳什均衡的问题。这一问题在纯策略中常会碰到。Allowing for mixed strategies in a game solves the problem of possible nonexistence of Nash equilibrium, which we encountered for pure strategies, automatically and almost entirely.著名的纳什定理表明：在一个相当一般的条件下，混合策略的纳什均衡定会存在。Nash ’s celebrated theorem shows that, under very general circumstances, a Nash equilibrium in mixed strategies exists.不确定性行为：为迷惑对手而混合策略Uncertain Actions: Mixing Moves to Keep the Opponent Guessing
当所有参与者都只有两个基础的纯策略时，混合策略其实就是一种特殊的连续变量策略。When all the players have only two underlying pure strategies, mixed strategies are a special kind of continuously variable strategy.因而可以使用最优反应分析。
Thus we can use the same solution method –best response analysis.
豫公网安备41160202000603
站长QQ:729038198
关于我们
投诉建议