pay off matrix

简明释义

支付矩阵

英英释义

例句

1.In game theory, the concept of a pay off matrix 收益矩阵 helps to analyze the strategies of competing players.

在博弈论中，pay off matrix 收益矩阵的概念有助于分析竞争玩家的策略。

2.During the negotiation, the team referred to a pay off matrix 收益矩阵 to determine the best offer.

在谈判过程中，团队参考了一个pay off matrix 收益矩阵以确定最佳报价。

3.The business team used a pay off matrix 收益矩阵 to evaluate the potential outcomes of their marketing strategies.

业务团队使用了一个pay off matrix 收益矩阵来评估他们营销策略的潜在结果。

4.Understanding the pay off matrix 收益矩阵 is crucial for making informed decisions in competitive markets.

理解pay off matrix 收益矩阵对于在竞争市场中做出明智的决策至关重要。

5.The pay off matrix 收益矩阵 indicated that cooperation would yield better results than competition.

该pay off matrix 收益矩阵表明，合作将产生比竞争更好的结果。

作文

In the realm of decision-making, particularly in economics and game theory, one often encounters the term pay off matrix. A pay off matrix is a tool used to illustrate the potential outcomes of various strategies employed by different players in a game. It provides a clear and concise representation of how each player's choices can lead to different results, depending on the actions of their opponents. This concept is crucial for understanding competitive behavior and making informed decisions in uncertain situations.To illustrate the significance of a pay off matrix, let’s consider a classic example known as the Prisoner’s Dilemma. In this scenario, two criminals are arrested and interrogated separately. They have two choices: to cooperate with each other by remaining silent or to betray the other by confessing. The pay off matrix for this situation can be laid out as follows:- If both remain silent, they each serve 1 year in prison.- If one betrays while the other remains silent, the betrayer goes free while the silent one serves 3 years.- If both betray each other, they each serve 2 years.The pay off matrix helps to visualize these outcomes:| | Cooperate (Silent) | Betray (Confess) ||--------------|--------------------|------------------|| Cooperate | (-1, -1) | (-3, 0) || Betray | (0, -3) | (-2, -2) |In this matrix, the first number in each pair represents the years served by Player A, while the second number represents the years served by Player B. The dilemma arises because, despite the best outcome occurring when both players cooperate, the rational choice for each individual leads them to betray the other, resulting in a worse outcome overall.Understanding the pay off matrix is vital not only in theoretical scenarios but also in real-world applications. Businesses often use similar matrices to evaluate competitive strategies. For instance, two companies may decide whether to lower their prices or maintain them. The pay off matrix can help them analyze their options and predict the potential reactions of their competitors, guiding them toward more strategic decisions.Moreover, the pay off matrix can extend beyond binary choices. In more complex games involving multiple players and strategies, the matrix can become a multi-dimensional array, still serving the same purpose: to clarify the potential outcomes based on various actions taken by the participants.In conclusion, the pay off matrix is an invaluable tool in the fields of economics, game theory, and strategic decision-making. By providing a structured way to analyze the consequences of different choices, it enables individuals and organizations to navigate complex interactions effectively. Whether in competitive business environments or theoretical dilemmas, understanding the implications of a pay off matrix can lead to better decision-making and improved outcomes. As we continue to face choices that involve uncertainty and competition, the ability to utilize a pay off matrix will remain a crucial skill for success.

在决策领域，特别是在经济学和博弈论中，人们常常会遇到术语支付矩阵。支付矩阵是用来说明不同参与者在博弈中采用的各种策略潜在结果的工具。它提供了一种清晰简洁的方式，展示每个玩家的选择如何根据对手的行为导致不同的结果。这个概念对于理解竞争行为和在不确定情况下做出明智的决策至关重要。为了说明支付矩阵的重要性，让我们考虑一个经典的例子，称为囚徒困境。在这个场景中，两名罪犯被逮捕并分别审讯。他们有两个选择：通过保持沉默来合作，或者通过认罪来背叛对方。这个情况的支付矩阵可以如下列出：- 如果两人都保持沉默，他们各自服刑1年。- 如果一人背叛而另一人保持沉默，背叛者将获释，而沉默者将服刑3年。- 如果两人都背叛对方，他们各自服刑2年。支付矩阵帮助可视化这些结果：| | 合作（沉默） | 背叛（认罪） ||--------------|--------------------|------------------|| 合作 | (-1, -1) | (-3, 0) || 背叛 | (0, -3) | (-2, -2) |在这个矩阵中，每对数字中的第一个数字表示A玩家服刑的年数，而第二个数字表示B玩家服刑的年数。困境的出现是因为，尽管当两个玩家都合作时获得的最佳结果，但每个人的理性选择却导致他们背叛对方，从而导致整体结果更差。理解支付矩阵不仅在理论场景中至关重要，而且在现实世界应用中也同样重要。企业经常使用类似的矩阵来评估竞争策略。例如，两家公司可能决定降价或维持价格。支付矩阵可以帮助它们分析选项并预测竞争对手的潜在反应，从而指导它们做出更具战略性的决策。此外，支付矩阵可以扩展到超出二元选择的范围。在涉及多个玩家和策略的更复杂的博弈中，矩阵可以变成多维数组，仍然发挥同样的作用：澄清基于参与者采取的各种行动的潜在结果。总之，支付矩阵在经济学、博弈论和战略决策领域是一个无价的工具。通过提供一种结构化的方式来分析不同选择的后果，它使个人和组织能够有效地应对复杂的互动。无论是在竞争的商业环境中还是在理论困境中，理解支付矩阵的含义都能导致更好的决策和改善的结果。随着我们继续面临涉及不确定性和竞争的选择，利用支付矩阵的能力将始终是成功的关键技能。