夏普利匹配理论是什么

夏普利匹配理论（Shapley Value）是博弈论中的一种重要概念，用于解决合作博弈问题。该理论由美国经济学家、诺贝尔经济学奖得主罗伊德·夏普利（Lloyd Shapley）在1953年提出，被广泛应用于各个领域，包括经济学、政治学、社会学等。

夏普利匹配理论的核心思想是在合作博弈中，每个参与者应当获得其“贡献”的公平份额。这里的“贡献”是指参与者在合作中带来的价值，以及与其他参与者进行合作的潜在价值。夏普利匹配理论通过精确地量化每个参与者的贡献，为合作博弈中的利益分配提供了公平和合理的依据。

夏普利匹配值的计算基于“核心”和“核值”的概念。在合作博弈中，如果所有参与者都能获得大于或等于其贡献的收益，则称该收益分配方案位于“核心”。而“核值”则是指对于每个参与者来说，其在所有可能的收益分配方案中最小的收益。夏普利匹配值就是核值的加权平均值，其中权重为每个参与者与其他参与者进行合作的潜在价值。

夏普利匹配理论具有很多重要的性质，例如它满足了个体理性和集体理性，即每个参与者的收益都不低于其贡献，且所有参与者的总收益等于所有参与者的总贡献。此外，夏普利匹配还是唯一的，这意味着在给定合作博弈的结构下，每个参与者的夏普利匹配值是唯一确定的。

总的来说，夏普利匹配理论是一种重要的博弈论工具，用于解决合作博弈中的利益分配问题。它通过精确地量化每个参与者的贡献，为合作博弈中的利益分配提供了公平和合理的依据。夏普利匹配理论的应用范围广泛，不仅在经济学领域有着重要的应用价值，在其他领域也有着广泛的应用前景。

英文：What is the Shapley Value?

The Shapley Value is a key concept in Game Theory that is used to solve cooperative博弈problems. It was proposed in 1953 by Lloyd Shapley, an American economist who won the Nobel Prize in Economics. The Shapley Value has been widely applied in various fields, including economics, politics, sociology, and more.

The core idea of the Shapley Value is that in cooperative games, each participant should receive a fair share of the "contribution" they make. The "contribution" refers to the value that participants bring to the collaboration, as well as the potential value of their cooperation with other participants. The Shapley Value provides a fair and reasonable basis for the distribution of benefits in cooperative games by quantifying each participant's contribution precisely.

The calculation of the Shapley Value is based on the concepts of the "core" and "core value". In a cooperative game, if all participants can receive a payoff that is greater than or equal to their contribution, the payoff distribution is said to be in the "core". The "core value" refers to the minimum payoff for each participant across all possible payoff distributions. The Shapley Value is the weighted average of the core values, with weights given by the potential value of each participant's cooperation with others.

The Shapley Value has several important properties. It satisfies individual rationality and collective rationality, meaning that each participant's payoff is not less than their contribution, and the total payoff for all participants is equal to the total contribution of all participants. Additionally, the Shapley Value is unique, which means that given the structure of a cooperative game, each participant's Shapley Value is uniquely determined.

In summary, the Shapley Value is an important tool in Game Theory that is used to solve the problem of benefit distribution in cooperative games. It provides a fair and reasonable basis for the distribution of benefits by precisely quantifying each participant's contribution. The Shapley Value has important application value not only in the field of economics, but also has broad application prospects in other fields.