  Methods of merging several p-values into a single p-value are important in
their own right and widely used in multiple hypothesis testing. This paper is
the first to systematically study the admissibility (in Wald's sense) of
p-merging functions and their domination structure, without any information on
the dependence structure of the input p-values. As a technical tool we use the
notion of e-values, which are alternatives to p-values recently promoted by
several authors. We obtain several results on the representation of admissible
p-merging functions via e-values and on (in)admissibility of existing p-merging
functions. By introducing new admissible p-merging functions, we show that some
classic merging methods can be strictly improved to enhance power without
compromising validity under arbitrary dependence.
