… , but instead of reporting their types (or complete utility functions), agents only report a two-…
( x i ) the social welfare function, which is a strictly increasing concave function. We will require …

… We also write s S, c  fi for s S fi, sc fi  fi. … maximiser of the weighted utilitarian social
welfare function Ri2N p√ … derived from the maximisation of a Social Welfare Ordering (for in that …

… a social choice function f is virtually implementable in Nash … Nash implementation it has
been known since Maskin's work … Maskin-type mechanisms depend critically on being able to …

… Furthermore, the Nash welfare function has been used … When there is only one type the
instance is identical and we … Approximating Nash social welfare under submodular valuations …

… Additionally, any outcome in which one player plays an element of V or C has social welfare
… The utility functions we choose in fact do not depend on the types, so we omit the type …

… institutions play in the organization of economic, political, and social … such as equilibrium
concepts and social welfare functions. … Here, we take the view that the kind of problems that may …

… ) for firms of type 1 and 2 behaving in a Cournot-Nash way in the … type 2 to zero: 7i2((, 9(())
= 0. Step 6: For a small enough, in a pseudo a-yi-Cournot-Nash equilibrium the profit function …

… utility functions ui are concave on S. We have shown that the Nash welfare function satisfies
… implicit assumptions behind the Nash equilibrium concept: what kind of assumptions imply …

… Motivated by examples of this type concerning the internet, Koutsoupias and Papadimitriou
[5… , submodular, social utility function we will show that any Nash equilibrium has an expected …

… social welfare functions are characterized by the weak Pareto principle, a continuity axiom,
and the following informational robustness property: the social … Nash social welfare functions …