Nash social welfare
Nash social welfare function
#game_theory #economics
#game_theory #economics
Definition (Kaneko and Nakamura 1979)
Suppose a social preference relation satisfying von Neumann-Morgenstern utility axioms, .
#incomplete
Definition
may define as geometric mean of valuations of 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 [[utility function|valuation]] which is [[monotone function|monotone]] ## Notes - arises in _social choice theory_ - see [[maximum Nash welfare]], [[envy-freeness]], _social welfare function_, _Arrow's theorem_ - compare [[Pareto optimal|Pareto optimality]] --- ## References 1. https://www.cs.cmu.edu/~csd-phd-blog/2025/fair-allocation-nash-welfare/ 2. M. Kaneko and K. Nakamura, “The Nash Social Welfare Function,” _Econometrica_, vol. 47, no. 2, p. 423, Mar. 1979, doi: [10.2307/1914191](https://doi.org/10.2307/1914191). ParseError: Can't use function '$' in math mode at position 31: …v_i(x_i))^{1/n}$̲$ whereas each …