This article has proved the existence of equilibrium prices for Bertrand competition with multi-product firms under the Logit model without restrictive assumptions on the firms or their products. Instead of studying a particular utility function, ge…

With Theorem 1, we have taken a significant step in understanding the structure of algorithmic information in Euclidean spaces. Progress in that direction is especially consequential in light of Theorem 12, which, aside from its direct value as a ma…

Some of this work was done while Leslie Hogben was a general member of the Institute for Mathematics and its Applications (IMA) and during a week-long visit of Kevin Palmowski to IMA; they thank IMA both for financial support (from NSF funds) and fo…

Many, if not most, approaches to establish cospectrality rely on showing that a small perturbation in the graph corresponds to a small, controllable perturbation in the eigenvectors and hence eigenvalues are preserved. This was not the case in this …