Are loyalty-rewarding pricing schemes anti-competitive?

Many economists and policy analysts seem to believe that loyalty-rewarding pricing schemes, like frequent flyer programs, tend to reinforce firms' market power and hence are detrimental to consumer welfare. The existing academic literature has supported this view to some extent. In contrast, we argue that these programs are business stealing devices that tend to enhance competition, in the sense of generating lower average transaction prices and higher consumer surplus. In highly competitive environments this result is robust to alternative specifications of the firm' commitment power and demand structures. However, it could be reversed if the number of firms is sufficiently small and if firms are restricted to use program designs with sufficiently weak commitment capacity.