*John Nash program is alive!*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.

**All Going for the Blonde is a Nash equilibrium but not a Nash solution**

*A Beautiful Mind*(based on the book of the same title by Sylvia Nasar) about the life of John Nash. A group of four students, including Nash, are spending some time in a bar in Princeton when five girls, including a stunning blonde, enter the room. Nash says, “If we all go for the blonde, we block each other and not a single one of us is gonna get her.” He suggests that “no one goes for the blonde,” and that the four boys instead pair up with the other girls –to the bemusement of his fellow students.

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

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