We are happy to have won.

[lagoo]

(1) We are happy to have won.
(2) We are happy to win.

Sentence (1) either means 'we have just won a match and we are now very happy', or 'we won a match a couple of day ago, but we are still happy now'.
Sentence (2) means 'we just win a match', and might imply 'we are still in the field, waiting for the champion celebration'.

Is my analysis right, or are they identical that you can choose whichever one you like?

 

[GoesStation]

The speakers are currently happy in sentence one, but the winning that elevated their mood could have occurred at any time in the past.

I can't think of an everyday context where sentence two would be natural.

 

[jutfrank]

We are happy to win.

I want to interpret this to mean something like We don't mind winning, which seems quite an unlikely thing to say.

 

[lagoo]

...which seems quite an unlikely thing to say.

The 23-year old was emotional after winning the bronze medal dedicating it to his late father Charles Edmund, who passed away last year.
"Getting a medal means a lot and I dedicate it to my late dad who passed away last year," Seghers said, "I am happy to win a medal for him and for PNG and I want to thank the people for coming out to support us."
link https://www.thenational.com.pg/seghers-dedicates-win-to-dad/

This is similar to my OP.
So that means you should say "I am happy to have won a medal for him" for the bold part, as is known from the context that the speaker has already won the medal.
Am I right?

 

[Roman55]

Given the wider context, the 'happy to win...' is OK because it is being said as the medal is being awarded.

 

[Tdol]

I think I would still have used to have won there, though.