Example-2.jsx

<CompareWrapper>
  {this.renderPlayers}
</CompareWrapper>

renderPlayers(playerIDs, addPlayer) {
  return playerIDs.map((playerID) => 
      <PlayerWrapper id={playerID}>
        {(player) => this.renderPlayer(player, addPlayer)}
      </PlayerWrapper>            
    )
}

renderPlayer({name, picture}, addPlayer) {
  return (
    <Player name={name} picture={picture}>
      <Button onPress={() => addPlayer(otherPlayerId)}></Button>
      <Table>{/*(...)*/}</Table>
    </Player>
  );
}

Example.jsx

<CompareWrapper>
  {(playerIDs, addPlayer) => 
      playerIDs.map((playerID) => 
        <PlayerWrapper id={playerID}>
          {({name, picture}) => 
            <Player name={name} picture={picture}>
              <Button onPress={() => addPlayer(otherPlayerId)}></Button>
              <Table>{/*(...)*/}</Table>
            </Player>}
        </PlayerWrapper>            
      )
  }
</CompareWrapper>