A bit tricky for me to name a team of the tournament, since I've missed a lot of games and not always played close attention to defenders in teams I don't know well. I'll have a go though. Here's my first draft to get some discussion going. Attack: Sanchez, Vargas and Messi. Midfield: James Rodriguez, Vidal, Dempsey, Jhasmani Campos. Defence: Beusajour (at left back), Otamendi, + 1 Peru defender. Keeper: Bravo. Subs: Romero, Mascherano (for this final performance), Marquez (I was impressed when he appeared to score a key goal as I assumed was he retired by now), Godin, Lavezzi, Higuain, Rondon. I am not really convinced about a lot of my choices. James Rodriguez was not as good as the world cup for sure, but he still looked quality at times, and probably Colombia's best player, and had to pick at least one player from each semi finalist. Dempsey I am putting in midfield instead of attack just so the team isn't ridiculously attacking. Jhasmani Campos mostly because I think he scored the goal of the tournament, although I did watch him more closely for the rest of the game after that and I thought he was good. Otamendi was an ever present I think in an Argentina defence that barely conceded a goal. I think we need 1 Peruvian defender after they shut out Colombia and Brazil. Not sure which one though. Bravo for the great game in the final and 3 clean sheets in a row in the knockout stages, although he was really poor in one group game, so maybe Romero or someone else deserves it more (?).
Maybe Mercado for right back for Argentina, just because they were a solid defence and I need a right back. I didn't really notice him at all, but I suppose that's not a bad thing for a full back.
https://www.theguardian.com/football/blog/2016/jun/27/copa-america-2016-highlights-lionel-messi There are some teams of the tournament in here, if you scroll down
I'm surprised they didn't release a 23 man selection. Dempsey and Brooks for sure would have made that
Maybe Mercado for right back for Argentina, just because they were a solid defence and I need a right back.