Tucker's well-known combinatorial lemma states that for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {+/-1,+/-2,...,+/-n} with the property that antipodal vertices on the...

In this paper three sufficient conditions are provided under each of which an upper semi-continuous point-to-set mapping defined on an arbitrary polytope has a connected set of zero points that connect two distinct faces of the polytope. Furthermore, we obtain an existence theorem of a connected...

Let X be a non-empty, compact, convex set in R and o an upper semi-continuous mapping from X to the collection of non-empty, compact, convex subsets of R;. It is well known that such a mapping has a stationary point on X, i.e. there exists a point in X satisfying that its image under o has a...

We present a polynomial time method for identifying the maximal set in excess demand at a given payoff vector. This set can be used in “large” partnership formation problems to identify the minimum element in the set of individually rational payoff vectors at which there is no overdemanded...

This paper investigates hypotheses related to efficiency and price uniformity in online competing auctions based on two theoretical predictions from Peters and Severinov [Peters, M., Severinov, S., 2006. Internet auctions with many traders. Journal of Economic Theory 130, 220–245]. The...