Much like alkenes, alkyne will also undergo addition to alkyne.
A few mechanism have been considered and come into play depending upon the structure of the alkyne.
Aryl alkynes tend to proceed through a vinylcation intermediate since a mixture of syn and anti addition poducts are observed. A vinyl carbocation would be stabilized in such cases by the adjacent aryl group.
The bromide anion can attack either side of the vinyl cation resulting in both syn and anti-products.
Alkyl alkynes reactivity depends upon whether they are internal or terminal alkynes. Internal alkynes tend to undergo anti-addition, which is consistent with a termolecular or bridged halonium ion. Terminal alkynes likely proceed through a vinyl cation intermediate.
In a termolecular process, two Br2 molecules react simultaneously with the alkyne.
Termolecular Process
Bridged Halonium ion