Every man inherits his haplo-type from his father, and thus the male lineage can be traced back.
Given a population $n$ males,
At each generation we uniformly sample $n$ males (with repetitions) to be the fathers of the next male generation.
After how many generations will the population converge to only one haplo-group ?
On
Not the complete answer but something to help you get started.
Let's write the probability to go from $k$ different haplo-types to $l<k$ haplo-types in one step, when there are $n$ initial haplo-types. We get the probability (the reasoning can be found in this answer): $$\Pr[k\to l;n] = \frac{n!S_{n,l}}{(k-l)!\times k^n}$$ with $S_{n,l}$ denoting the Stirling number of the second kind.
To get the probability expected number of surviving haplo-types at the beginning of the second step, you can use the formula $\sum_{i=1}^{n}i \times Pr[n \to i;n]$.
Using these probabilities you can describe your problem as a Markov Chain, from which you can estimate the expected time it takes to eliminate all but one haplo-type.
This is the Wright-Fisher model. You can find the expected time for one type to take over the population on Wikipedia, or, if you want something more official, Ewens' Mathematical population genetics, eqn. (3.11). It's $E[T]=-2n^2(1-1/n)\log(1-1/n)$, which is $E[T]\approx 2n$ for $n\gg 1$.