Traditional interdomain routing algorithms such as Border Gateway Protocol (BGP) rely on bilateral peering agreements between service providers to support end-to-end connectivity in the Internet. Network end users have very little control in the selection of these routes. Instead, network users are given a route to their destination with little or no assurances on its availability or performance. This traditional approach is not likely to work well for many rapidly growing streaming and gaming applications because their performance benefits significantly from better-than-best-effort connectivity. One possible approach for supporting such connectivity is to rely on a market-based mechanism through which network end users can shop and purchase interdomain routes of their choice. This paper envisions such a market in the near future. The paper then proposes a pricing strategy for connectivity service providers, called PriceMyRoute. The strategy allows multiple service providers to effectively compete with each other in order to offer the end-to-end connections requested by network users. The approach is likely to succeed because: (i) it offers monetary compensation to service providers for providing the routing flexibility to network users, and (ii) the improved performance is an incentive for network users to purchase better-than-best-effort end-to-end connectivity. The paper compares the effectiveness of the proposed strategy with that of RouteBazaar, a recent related scheme from literature . The comparison shows that both service providers and network users are likely to be more satisfied using the proposed strategy as compared to RouteBazaar.