Structural Analysis of Two Person Game with Mixed Strategy for Delivery Services : How to Decide Service Area and Pricing Strategy(Theory and Methodology)

Abstract

We consider a class of delivery services, in which products are delivered to customers under the following two conditions: 1) each supplier must offer its own uniform price to all customers regardless of possibly different transportation costs; 2) each supplier offers its delivery service to a customer only when it results in a positive return. A competitive market of this sort with two suppliers and two (grouped) customers is formulated as a symmetric two person game. With a set of mixed strategies defined on a certain set of L discrete points, it is shown that two types of Nash equilibriums exist and can be constructed explicitly. Furthermore, such Nash equilibriums converge to the mixed strategies defined on a continuum, which are also Nash equilibriums, as L→∞.