ON SEMI-VALUATIONS. I.

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

Iterative Auction Design for Graphical Valuations Part I: Tree Valuations∗

In this work, we design simple and e cient iterative auctions for selling multiple items in settings where bidders’ valuations belong to a special class (tree valuations) that can exhibit both value complementarity and substitutability. Our first contribution is to provide a compact linear programming formulation of the e cient allocation problem and use it to establish the existence of a Walra...

Theory of valuations on manifolds , I . Linear spaces .

This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of an affine space. In this article we still work only with linear spaces. We introduce a space of smooth (non-translation invariant) valuations on a linear space V . We present three descriptions of this spac...

Realization of a certain class of semi-groups as value semi-groups of valuations

Given a well-ordered semi-group Γ with a minimal system of generators of ordinal type at most ωn 1 and of rational rank r, which satisfies a positivity and increasing condition, we construct a zero-dimensional valuation centered on the ring of polynomials with r variables such that the semigroup of the values of the polynomial ring is equal to Γ. The construction uses a generalization of Favre ...

realization of a certain class of semi-groups as value semi-groups of valuations