The prospects headed to the Athletics are left-hander Jesus Luzardo and third baseman Sheldon Neuse.
The Nationals have been looking for help at the back end of their bullpen. Treinen, 29, is 0-2 with a 5.73 ERA and two saves in 37⅔ innings. He is one of six pitchers with at least two saves for Washington, but nobody has more than Koda Glover‘s eight, and he is on the disabled list.
Doolittle, 30, is 1-0 with a 3.38 ERA and three saves in 21⅓ innings. He had a career-high 22 saves in 2014.
Madson, 36, is 2-4 with a 2.06 ERA and one save in 39⅓ innings. He had 30 saves for Oakland last season.
Luzardo, 19, is a 2016 third-round draft pick who has made three starts in rookie ball this season, going 1-0 with a 1.32 ERA.
Neuse, 22, was a second-round draft pick in 2016 and was ranked as the Nationals’ No. 7 prospect before the season. He is hitting .291 with nine homers and 51 RBIs for Class A Hagerstown.