Merging sequential e-values via martingales

We study the problem of merging sequential or independent e-values into one e-value for statistical decision making. We describe a class of e-value merging functions via martingales, and show that all merging methods for sequential e-values are dominated by such a class. In case of merging independent e-values, the situation becomes much more sophisticated, and we provide a general class of such merging functions based on reordered test martingales.