Actually, I think it's asymmetrical. I don't think CaBi sees Metro as the enemy, particularly since they are a useful tool for the "last mile" problem. OTOH, Metro has publicly stated that part of their ridership decline can be attributed to more bicycling, including Capital Bikeshare.
The general concept of integrating forms of transit is, in and of itself, a good idea. It's already done a lot--particularly between buses and rail. So I think PotomacCyclist raising this idea can make for a worthwhile discussion. Since CaBi can be a good "last mile" solution for other forms of transit, linking them somehow makes good sense.
One simpler, starter idea in this regard might be cross marketing of some kind. For instance, Metro riders could get coupons for a free ride on CaBi. To reduce the free-riders problem, they could be limited to same day and certain CaBi stations. That sort of thing. If the goal is to help people better understand the connectedness the systems can create, with the intent of increasing use of both systems, then unleash some marketing geniuses to come up with promos and other tools to work on that. Shared fare systems is just one idea of many that could be considered.
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