Must-Take Cards: Merchant Discounts and Avoided Costs

Antitrust authorities often argue that merchants cannot reasonably turn down payment cards and therefore must accept excessively high merchant discounts. The paper attempts to shed light on this “must-take cards” view from two angles. First, the paper gives some operational content to the notion of “must-take card” through the “avoided-cost test” or “tourist test”: would the merchant want to refuse a card payment when a non-repeat customer with enough cash in her pocket is about to pay at the cash register? It analyzes its relevance as an indicator of excessive interchange fees. Second, it identifies four key sources of potential social biases in the payment card systems’ determination of interchange fees: internalization by merchants of a fraction of cardholder surplus, issuers’ per-transaction markup, merchant heterogeneity, and extent of cardholder multi-homing. It compares the industry and social optima both in the short term (fixed number of issuers) and the long term (in which issuer offerings and entry respond to profitability)

Period polynomials and Ihara brackets

Schneps [J. Lie Theory 16 (2006), 19--37] has found surprising links between Ihara brackets and even period polynomials. These results can be recovered and generalized by considering some identities relating Ihara brackets and classical Lie brackets. The period polynomials generated by this method are found to be essentially the Kohnen-Zagier polynomials.Comment: 12 pages, LaTE

The # product in combinatorial Hopf algebras

We show that the # product of binary trees introduced by Aval and Viennot [arXiv:0912.0798] is in fact defined at the level of the free associative algebra, and can be extended to most of the classical combinatorial Hopf algebras.Comment: 20 page

On parsimonious edge-colouring of graphs with maximum degree three

In a graph $G$ of maximum degree $\Delta$ let $\gamma$ denote the largest fraction of edges that can be $\Delta$ edge-coloured. Albertson and Haas showed that $\gamma \geq 13/15$ when $G$ is cubic . We show here that this result can be extended to graphs with maximum degree 3 with the exception of a graph on 5 vertices. Moreover, there are exactly two graphs with maximum degree 3 (one being obviously the Petersen graph) for which $\gamma = 13/15$. This extends a result given by Steffen. These results are obtained by using structural properties of the so called $\delta$-minimum edge colourings for graphs with maximum degree 3. Keywords : Cubic graph; Edge-colouringComment: Revised version submitted to Graphs and Combinatoric

Survival probability of the branching random walk killed below a linear boundary

We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and bounded random walk steps. Connections with the Brunet-Derrida theory of stochastic fronts are discussed