Get multiple nested values from XML file using PHP

I'm working on a little project of mine, which involves an API from a video game, and I want to get stats from players from certain matches. The XML file from a certain match looks like this:

<result>
   <players>
      <player>
         <name>NAME1</name>
         <position>POSITION1</position>
         <age>AGE1</age>
      </player>
      <player>
         <name>NAME2</name>
         <position>POSITION2</position>
         <age>AGE2</age>
      </player>
      <player>
         <name>NAME3</name>
         <position>POSITION3</position>
         <age>AGE3</age>
      </player>
   </players>
   <winning_team>TEAM1</winning_team>
   <duration>DURATION</duration>
</result>

Now, I want to run through every player and see if that players name is i.e. 'Chris', how do I go about doing this? I thought about doing something like this:

    foreach($match_info->result->players->player as $player)
    {
        if($player->name == 'Chris')
           echo 'I found Chris';
    }

For more information, I'm using SimpleXMLElement to get the data from the XML file, and this works fine getting the winning_team and the duration, but I can't seem to figure out how to the get to the player names and then compare them all.