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所在平台: Udemy |
课程主页: https://www.udemy.com/course/game-theory-in-operations-research-and-decision-making/
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课程名称：运筹学与决策中的博弈论 课程概述： 本课程旨在深入研究博弈论的基础知识及其在冲突与竞争环境中的应用。博弈论是关于在多个理性对手参与的情况下进行决策的理论。学生将学习到以下内容：博弈的概念、鞍点、支配规则、修正支配规则、奇偶方法、图形法、子博弈法、代数法以及问题的公式化。 课程特点： 1. 竞争者人数有限。 2. 玩家采取理性和智能的行为。 3. 每位玩家都有有限的可能行为选择。 4. 玩家努力最大化收益和最小化损失。 5. 博弈结果受到所有玩家选择的影响。 6. 每位参与者都知道其对手的可选方案。 7. 博弈在每位玩家选择其行为时进行。 8. 各种行为组合决定结果，带来收益或损失给每位玩家。 9. 存在一套规则决定博弈的价值。 博弈论的概念与术语： 1. 玩家：每个参与者称为一个玩家。 2. 开局：当每位玩家选择行为时，称为博弈的开局。 3. 策略：玩家选择备选方案的规则，考虑所有可能的选择模式。 4. 纯策略：玩家在游戏中总是选择相同行为。 5. 混合策略：在固定概率下选择多种行为的决策。 6. 博弈价值：两名玩家使用最佳策略时的预期收益（或损失）。 7. 二人零和博弈：两个参与者之间利益完全对立的博弈，一个玩家的收益等于另一个玩家的损失。 8. 收益：博弈结果称为收益，反映策略给予玩家的净收益或损失。 9. 收益矩阵：展示不同策略结果的矩阵称为收益矩阵。 10. 鞍点：博弈的均衡点，最大最小值等于最小最大值。 11. 最大最小原则：玩家采取悲观态度，选择对应于最小收益的最大策略。 最小最大原则：选择对应于最大损失的最小策略。 该课程将帮助学生理解博弈论的基本原理及其在决策中的实际应用。
The term game represents a conflict between two or more parties.Game Theory may be defined as the body of knowledge that deals with making decisions when two or more intelligent and rational opponents are involved under conditions of conflict and competition. In this course, the students will learn:Concept of GameSaddle PointDominance Rule Modified Dominance RuleOddoment MethodGraphical MethodSub Games MethodAlgebraic MethodProblem FormulationLets discuss some Characteristics of Games1.The number of competitors is finite.2. The player act rationally and intelligently.3. Each player has available to him a finite set of possible courses of action.4. The players attempt to maximize gains and minimize losses.5. The outcome of the game is affected by the choices made by all the players.6. Every participant has the knowledge above the alternatives available to his opponent.7. A game is played when each player chooses his one course of action.8. Every combination of courses of action determines an outcome which results in a gainor loss to each player.9. There exits a set of rules according to which the value of game will be determined.Concepts & Terminology in Game Theory1) Player- Each participant (party) is called a player.2) Play- A play of the game results when each player has chosen a course of action.3) Strategy- A rule or set of rules on the basis of which a player selects his alternative. It refers to the total pattern of choices employed by any player.4) Pure strategy- A pure strategy is a decision always to select the same course of action when a player plays one row all of the time or one column all of the time in case of player 4), he is said to be playing a pure strategy.5) Mixed strategy - Mixed strategy is a decision to select more than one of his course of action with fixed probabilities. In a mixed strategy, player A will play each of his rows a certain portion of the time and player Y will play each of his columns a certain part of time.6) Value of the game- The value of the game is the expected gain(or loss) of both the players , if both players use their best strategies.7) Two person zero sum game-Two person zero sum game are played by two persons, parties or groups, with directly opposing interests. One person's gain is exactly equal to the loss of another player and therefore the sum total of the gain and loss is equal to zero.8) Payoff- The outcome of playing the game is known as payoff. It is the net gain or loss the strategy brings to the player.9) Payoff matrix- The table/matrix representing the outcome or payoff of different strategies of the game is known as payoff matrix.10) Saddle point-It is known as the equilibrium point of the game. Saddle point is the condition when maximin value is equal to the minimax value.It is called as the value of the game.11) Maximin Principle-According to this principle, The player adopts a pessimistic attitude. The maximizing player decides to play those strategies corresponding to the maximum of the minimum gains for his different courses of action.Minimax Principle-The minimizing player selects the strategies, which correspond to the minimum of the maximum losses for his different courses of action, which is referred to as Minimax principle.
