Showrooming and Shipping Costs in Price Competition between Online and Physical Stores

Today, consumers purchasing goods can choose between physical stores (or "brick-andmortar"stores) and online stores (or e-tailers). If a consumer purchases an unfamiliar good online, she is likely to receive a mismatched good. On the other hand, consumers who purchase goods from a physical store must incur the transportation costs and the shipping costs while major online stores generally do not pass on shipping charges to the consumers. Facing this dilemma, some consumers might go to a physical store for reducing mismatch; subsequently, they purchase the product from an online store to avoid the shipping charges. Such free-riding behavior of consumers is referred to as showrooming . This article analyzes showrooming and its effect on price competition between physical stores and online stores by formulating a spatial market model, and we show that one of two types of equilibrium might exist in the price competition, where some consumers display showrooming and others do not. In the model, we emphasize the role of shipping costs incurred by consumers only when they purchase goods from physical stores, which would determine the equilibrium that arises. In conclusion, both physical stores as well as online stores charge lower prices and obtain lower profits in equilibrium with showrooming than they do in equilibrium without showrooming

Elementary Proof of Schweitzer\u27s Theorem on Hilbert C*-Modules in which All Closed Submodules are Orthogonally Closed

Let A and B be C*-algebras and let X be an A-B-imprimitivity bimodule. Schweitzer showed the theorem that if every closed right B-submodule of X is orthogonally closed, then there are families {H_i}_, {K_i}_ of Hilbert spaces such that A (resp. B) is isomorphic to the C_0-direct sum Σ^*_C(H_i) of all compact operators C(H_i) on H_I (resp. Σ^*_C(K_i) of all compact operators C(K_i) on K_i) as a C^*-algebra, and X is isomorphic to the C_0-direct sum Σ^*_C(K_i, H_i) as a Hilbert C^*-module, where C(K_i,H_i) denotes the Hilbert C^*-module consisting of all compact operators from K_i into H_i. In this paper, we give an alternative proof, of this theorem, which is shorter and more elementary than the original one

An Alternative Proof of the Duality Theorem for Crossed Products of Hilbert C*-Modules by Abelian Group Actions

We give an alternative proof of the duality theorem for crossed products of Hilbert C-modules by abelian group actions by using the duality theorem for crossed products of Hilbert C-modules by coactions