在《作為公平的正義》中，羅爾斯在闡釋差別原則時提到的「納什點」和「邊沁點」是什麼意思？

N是納什點，在這裡功利的生產達到最大化，B是邊沁點，在這裡，個人功利的總量達到最大化。這句話是什麼意思

在此語境中，邊沁點代表了（以邊沁為代表的）古典效益主義目標的達成，其核心在於每一個個體的境遇獲得了最優化；而納什點代表了（以約翰·納什為代表的）博弈論最佳效益的均衡條件的達成，其核心在於整個集體的境遇獲得了最優化，也就是該條件能功利產出的最大化。換言之，羅爾斯對這兩個概念進行區分是為了比對以邊沁為代表的古典效益主義的個人功利最大化原則和以納什均衡為代表的集體效益最大化原則這兩種對「最優化條件」的理解。

（預設理解：效益主義傳統下「功利」概念的意涵）

更詳細的解釋請參看如下的二手文獻：

https://www.cambridge.org/core/books/the-cambridge-rawls-lexicon/nash-point/3B02DE6EDEA4A1F2D743ECE9C34FEF49

另將作者的總結附寫在此：

In explaining both the meaning of the difference principle and its choice by the parties in the original position, Rawls treats it as the solution to what is often called a bargaining game. He then contrasts the solution represented by the difference principle with other proposed solutions, in particular that of classical utilitarianism (what he calls the Bentham point) and that proposed by John Nash, the Nash point (JF 62–63).

In a bargaining game, players must divide up a pay-off between them, which they forfeit if they cannot agree. The size of the pay-off can be dependent on the agreement reached. Bargaining games capture essential features of social cooperation that raise the problem of distributive justice in the first place: social cooperation produces a surplus, but the size of the surplus is dependent on the rules governing the cooperation including how the surplus is to be divided.

In a bargaining game, any agreement that distributes all of the surplus will be what is called a Nash equilibrium: once adopted, there is no way for any player to improve her outcome by unilaterally changing her actions. The question is then which equilibrium point should be chosen. The difference principle can be thought of as a rule for choosing an outcome to the bargaining game. It says to choose the outcome that maximizes the pay-off to the worst off. Classical utilitarianism also yields a principle for choosing an outcome: it says, choose the outcome that maximizes the sum of the pay-offs, understood as utilities.

在解釋差異原則的含義和在最初狀態下各方的決策時，羅爾斯將它看作對於所謂的「議價博弈」的解決方案。此後，他將這種由差異原則代表的解決法案與其他人提出的方案進行比對，尤其是古典效益主義【的方案】（他稱之為「邊沁點」）和約翰·納什提出的方案——「納什點」（《作為公平的正義》，62-63）。

在議價博弈中，決策各方必須在他們之中瓜分報酬 (pay-off)；若他們不能達成統一則他們必須，該報酬必須被放棄。這份報酬的份額多少可以基於他們達成的共識。議價博弈體現了社會合作中最初引起分配公平問題的那些特徵：社會合作可以產出盈餘，但是改盈餘的多寡是基於合作所受限的規則的，譬如，盈餘應當怎樣被分配。

在議價博弈中，任何能將全部盈餘都分配到個人的共識都可以被稱為「納什均衡」(Nash equilibrium)：一旦被採納，任何一個個體都無法通過單向操作改善他自己的結果。那麼，問題是，【分配者】應該選擇哪一種均衡點？差異原則可以被看作一種選擇議價博弈結果的規則。它旨在選取一種使得境遇最差者的報酬最大化的結果。古典效益主義也能得出一種選取結果的原則：它說，【應該】選擇使得所有人獲得的報酬（在這一流派中被看作是「效益」）最大化的那種結果。

在Google的Cache中，發現知乎用戶 @米哈伊 回答過這個問題，不知道出於什麼原因，這個答案現在看不到了。米的答案的核心內容引用了劍橋羅爾斯辭典對Nash Point（納什點）的解釋。現轉錄如下：

Summary

In explaining both the meaning of the difference principle and its choice by the parties in the original position, Rawls treats it as the solution to what is often called a bargaining game. He then contrasts the solution represented by the difference principle with other proposed solutions, in particular that of classical utilitarianism (what he calls the Bentham point) and that proposed by John Nash, the Nash point (JF 62–63).

In a bargaining game, players must divide up a pay-off between them, which they forfeit if they cannot agree. The size of the pay-off can be dependent on the agreement reached. Bargaining games capture essential features of social cooperation that raise the problem of distributive justice in the first place: social cooperation produces a surplus, but the size of the surplus is dependent on the rules governing the cooperation including how the surplus is to be divided.

In a bargaining game, any agreement that distributes all of the surplus will be what is called a Nash equilibrium: once adopted, there is no way for any player to improve her outcome by unilaterally changing her actions. The question is then which equilibrium point should be chosen. The difference principle can be thought of as a rule for choosing an outcome to the bargaining game. It says to choose the outcome that maximizes the pay-off to the worst off. Classical utilitarianism also yields a principle for choosing an outcome: it says, choose the outcome that maximizes the sum of the pay-offs, understood as utilities.

根據這篇解釋，我們可以具體說一說怎麼理解題圖語境下的納什點和邊沁點。

邊沁點B的意思是，這個點最大化了所有人的總效用（效用之和）。對應於題圖，也就是OP曲線在B點的切線是一個以45度角向下傾斜的直線。

D點的意思是，這個點最大化了最不利者的效用。對應於題圖，也就是OP曲線在D點的切線與x軸平行。

納什點N的意思是，這個點上，合作產生的全部效用都被瓜分乾淨了，即任何人都沒有辦法在不損害別人的效用的前提下，來提升自己的效用。這種點的一個特性是，一旦被採納，任何一方都沒有辦法提出一個可以讓另一方甘心接受的新方案。在經濟學中，納什點被稱為納什議價的解（Nash Bargaining Solution）。

在納什1950年最初的公理化構造中，納什點N應當最大化所有人效用的幾何平均，題圖中的N點正是這樣一個點。在那裡，OP曲線的切線的斜率，其絕對值等於N點的縱坐標值對橫坐標值的比。這個比值在題圖中是小於1大於0的，因此，N點在D點的右邊，但卻在B點的左邊。

如果我們僅要求「合作產生的全部效用都被瓜分乾淨」這一條，即只要求帕累托最優，那麼題圖中的DF線段上的每一個點都滿足這樣的條件，包括封建點F，儘管在那裡，只有最有利者最大化了自己的效用。

Laden, A. (2014). Nash point. In J. Mandle D. Reidy (Eds.), The Cambridge Rawls Lexicon(pp. 546-547). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139026741.141