The two Somerset players were set to turn out for their national sides Scotland and Ireland in the final game of the Dubai Triangular Series in the UAE.
A win for Ireland would have seen them take the tournament trophy while Scotland still had a chance of winning on net run rate if they had come out on top.
Heavy rain and thunderstorms delayed the start, but hopes that they could still go ahead with a 20-over match were dashed when, just as play was about to start, it began to rain and the game was called off. Both sides took one point, which meant the trophy went to Ireland who topped the table with five points.
Davey finished the tournament with 75 runs in two innings, with a highest score of 53 not out. He also took six wickets for 74 runs at an average of 12.33, all of his wickets coming in his career best 6-28 against Afghanistan last week.
Dockrell meanwhile took five wickets in the tournament at 21.4, with a best performance of 4-35, which brought up his 50th wicket in one-day internationals.
The Dubai series was being played as a warm-up for next month’s ICC World Cup in Australia and New Zealand.