A decision algorithm to choose what partner to use
Techniques developed for the multi-armed bandit problem might be useful for discovering the partner with the best acceptance rate and dealing with the changing acceptance rate over time.  Those techniques balance "exploration" (sending transactions to a partner as a way to learn more information about their acceptance rate) vs "exploitation (sending transactions to the partner with the highest acceptance rate, to make use of the information gained previously).  You'll probably be especially interested in the non-stationary bandit problem.