Nash equilibrium

简明释义

纳什均衡

英英释义

例句

1.In auction settings, bidders often arrive at a Nash equilibrium 纳什均衡 when they bid according to their valuations without overbidding.

在拍卖环境中，竞标者通常在根据其估值出价而不超出预算时达到Nash equilibrium 纳什均衡。

2.In a two-player game, both players choosing the same strategy can lead to a Nash equilibrium 纳什均衡 where neither has an incentive to change their choice.

在一个两人游戏中，两位玩家选择相同策略可以导致一个Nash equilibrium 纳什均衡，在这个均衡中，没有人有动力去改变他们的选择。

3.The concept of Nash equilibrium 纳什均衡 is crucial in understanding how firms compete in oligopolistic markets.

理解公司在寡头市场中如何竞争时，Nash equilibrium 纳什均衡的概念至关重要。

4.When players in a traffic game choose their routes, they may settle into a Nash equilibrium 纳什均衡 where no one can reduce their travel time by changing paths.

当交通游戏中的玩家选择他们的路线时，他们可能会达到一个Nash equilibrium 纳什均衡，在这个均衡中，没有人通过改变路径来减少旅行时间。

5.The pricing strategies of competing firms often reach a Nash equilibrium 纳什均衡, where neither firm benefits from changing its price unilaterally.

竞争公司之间的定价策略通常会达到一个Nash equilibrium 纳什均衡，在这个均衡中，没有一家公司单方面改变价格会获益。

作文

In the realm of game theory, a concept that has garnered significant attention is the Nash equilibrium. This term refers to a situation in a strategic game where no player can benefit from changing their strategy while the other players keep theirs unchanged. The Nash equilibrium is named after John Nash, an American mathematician who made profound contributions to the field of economics and game theory. Understanding this concept is crucial for analyzing competitive situations where individuals or entities make decisions that affect one another. To illustrate the idea of Nash equilibrium, consider the classic example of the Prisoner's Dilemma. In this scenario, two criminals are arrested and interrogated separately. They can either cooperate with each other by remaining silent or betray each other by confessing. If both remain silent, they receive a minor sentence; if one betrays while the other remains silent, the betrayer goes free while the silent partner faces a harsh penalty. If both betray, they both receive a moderate sentence. The Nash equilibrium occurs when both criminals choose to betray each other, as neither can improve their situation by unilaterally changing their decision. This outcome, although not optimal for the pair, demonstrates how individual rationality can lead to collectively suboptimal results.The implications of Nash equilibrium extend beyond theoretical games; it can be applied to various real-world scenarios, including economics, politics, and social interactions. For instance, in an oligopoly market where a few firms dominate, each firm must consider the actions of its competitors when setting prices. If all firms reach a Nash equilibrium by setting prices at a certain level, none will benefit from changing their price unilaterally, as it would lead to losses in market share or profits.Furthermore, the concept of Nash equilibrium also plays a vital role in understanding social dilemmas. In environmental issues, for example, individuals may face a choice between polluting or conserving resources. If everyone chooses to pollute, the environment suffers, but if one person decides to conserve while others pollute, they may incur costs for no personal benefit. A Nash equilibrium may arise when individuals opt for pollution due to the belief that their individual efforts to conserve will not change the collective outcome.Critics of the Nash equilibrium argue that it does not always lead to the most efficient outcomes. In many cases, players may benefit from cooperation, but the fear of being exploited leads them to choose strategies that result in less favorable outcomes for all involved. This tension between individual rationality and collective welfare highlights the complexities of human behavior in strategic settings.In conclusion, the Nash equilibrium serves as a foundational concept in game theory, providing insights into decision-making processes in competitive environments. By understanding this equilibrium, we can better analyze situations where individual choices impact collective outcomes. Whether in economics, politics, or social dilemmas, recognizing the dynamics of Nash equilibrium allows us to navigate complex interactions and strive for more desirable outcomes, fostering cooperation where possible and understanding the limitations of individual rationality.

在博弈论的领域中，一个备受关注的概念是Nash equilibrium。这个术语指的是在一个战略游戏中，任何玩家在其他玩家保持其策略不变的情况下，都无法通过改变自己的策略而获得利益的情况。Nash equilibrium以美国数学家约翰·纳什的名字命名，他对经济学和博弈论领域做出了深远的贡献。理解这一概念对于分析个体或实体之间相互影响的竞争情境至关重要。为了说明Nash equilibrium的概念，可以考虑经典的囚徒困境例子。在这个场景中，两名罪犯被逮捕并分别审讯。他们可以选择通过保持沉默来互相合作，或者通过认罪来背叛对方。如果两人都保持沉默，他们会受到轻微的判刑；如果一个背叛而另一个保持沉默，背叛者将被释放，而保持沉默的伙伴将面临严厉的惩罚。如果两人都背叛，他们都会受到适度的判刑。Nash equilibrium发生在两个罪犯选择背叛对方时，因为在其他人不改变决定的情况下，任何一方都无法通过单方面改变自己的决定来改善自己的处境。这个结果，尽管对两人来说都不是最优的，但却展示了个体理性如何导致集体次优的结果。Nash equilibrium的影响超越了理论游戏；它可以应用于经济、政治和社会互动等各种现实场景。例如，在一个寡头垄断市场中，几家公司占据主导地位，每家公司在设定价格时必须考虑竞争对手的行为。如果所有公司通过在某个水平上设定价格达成了Nash equilibrium，那么没有公司会通过单方面改变价格而获益，因为这将导致市场份额或利润的损失。此外，Nash equilibrium的概念在理解社会困境中也发挥着重要作用。在环境问题中，例如，个人可能面临污染或节约资源的选择。如果每个人选择污染，环境就会遭受损害，但如果一个人决定节约而其他人污染，他们可能会因为没有个人利益而承担成本。当个人选择污染时，可能会出现Nash equilibrium，因为他们相信自己的节约努力不会改变集体结果。批评者指出，Nash equilibrium并不总是导致最有效的结果。在许多情况下，玩家通过合作可以受益，但对被利用的恐惧使他们选择导致所有人结果较差的策略。这种个体理性与集体福利之间的紧张关系突显了战略设置中人类行为的复杂性。总之，Nash equilibrium作为博弈论中的基础概念，为我们提供了对竞争环境中决策过程的深入洞察。通过理解这种均衡，我们可以更好地分析个体选择影响集体结果的情况。无论是在经济、政治还是社会困境中，认识到Nash equilibrium的动态使我们能够驾驭复杂的互动，努力追求更理想的结果，促进可能的合作，并理解个体理性的局限性。