KURSCHAK 1980 Problem 3

In a certain country there are two tennis clubs consisting of $1000$ and $1001$ members respectively. All the members have different playing strength, and the descending order of palying strengths in each club is known. Find a procedure which determines, within $11$ games, who is in the $1001$ st place among the $2001$ players in these clubs. It is assumed that a stronger player always beats a weaker one.