John F. Nash (1028-2015) was awarded the Nobel Prize in Economics in 1994. Most probably he was the Nobel winner with the fewest pages published in his life!. In three articles, he basically introduced two concepts. The so-called Nash equilibrium is the outcome of a game in which no player can improve his results by unilaterally changing his strategy.
Nash also introduced a normative concept, the “Nash solution,” for bargaining problems in which two or more actors try to reach an agreement on how to divide a good. The classical utilitarian criterion holds that the best social solution is the one that maximizes the sum of the actors’ utilities. This criterion inspires, for instance, the evaluation of the welfare of a country by its average per capita income or by the general level of citizens’ political satisfaction. In contrast, the Nash solution is the one that maximizes the product of the actors’ utilities.
A reasonable interpretation is the following. If only one person obtains the maximum prize, say with value 10, and the other three get nothing, the sum of the four actors’ utilities can be relatively high in comparison with an alternative outcome in which each of the four actors gets a lower value, say of only 2 (since 10 + 0 + 0 + 0 = 10 > 2 + 2 + 2 + 2 = 8). But the product of utilities in the first outcome is very bad (actually it is zero, since three actors get nothing and can be extremely frustrated), while the product of the latter is higher (2 * 2 * 2 * 2 = 16).
Generally, in comparison with the classical utilitarian “Bentham sum” solution, the “Nash product” solution favors more egalitarian distributions. For example, under the sum criterion, a distribution of values among three actors such as 3, 2, 1, is as good as the distribution 2, 2, 2 (since both imply a sum of 6 units of social utility). But under the product criterion, the former distribution (whose product is 3 * 2 * 1 = 6) is worse than the latter one (whose product is 2 * 2 * 2 = 8).
(Excerpt from my book: Colomer, The Science of Politics. An Introduction. Oxford UP CLICK)