… achieve some kind of balance between the efficiency of the maximum utilitarian social
welfare—… We first identify the subclasses of valuation functions for which the MNW allocations are …

… , we show a price of anarchy type result: for general concave … yields an approximate
CE for all concave utility functions; we … Nash social welfare for indivisible items under separable, …

… for calculating a social welfare but the Nash welfare seems to be … Nash welfare function, we
can see that this welfare function … , the acceptability criterion and the kind of deals that should …

… In this case, we could write each agent’s utility function as \(u_i(x_i) = \max _{p \in P_i} \min
_{j \in p} x_{ij}\), where \(P_i\) is the set of paths from agent i’s desired source to desired …

… The second question is whether the techniques introduced in this work generalize to
more general valuation functions, in particular, submodular valuations for the weighted …

… Let's now go back to the kind of exchange economy that we … Therefore, the Arrow social
welfare function induced by F … our attention to Arrow social welfare functions that map into the …

… functions are part of the input. The goal is to find an allocation of the goods A = (A1,...,An) to
maximize the Nash social welfare… We will consider two kinds of alternating paths in Gh : A- A-…

… a constraint both on the choice of procedures which can be used as decentralized decision
procedures and on the type of objective functions which can be 'achieved' or 'implemented' . …

… We discuss different kinds of aggregation procedures that have been studied in the literature.
… As a final remark, note that the three social welfare functions we defined above (utilitarian, …

… "mechanisms" or "outcome functions") the equilibria of which … of social welfare called a social
choice rule . A game form, in … can write each individual's equilibrium action as a function st(…