Nash social welfare

Nash social welfare function
#game_theory #economics

Definition (Kaneko and Nakamura 1979)

Suppose a social preference relation satisfying von Neumann-Morgenstern utility axioms, $R$ .

#incomplete

Definition

may define as geometric mean of valuations of $n$ agents, i.e.

(\prod_{i=1}^n v_i(x_i))^{1/n}

whereas each agent $i$ has a bundle $x_i$ and assigns it a valuation which is monotone

Notes

arises in social choice theory
see maximum Nash welfare, envy-freeness, social welfare function, Arrow's theorem
compare Pareto optimality

References

https://www.cs.cmu.edu/~csd-phd-blog/2025/fair-allocation-nash-welfare/
M. Kaneko and K. Nakamura, “The Nash Social Welfare Function,” Econometrica, vol. 47, no. 2, p. 423, Mar. 1979, doi: 10.2307/1914191.