Domain Driven Design of a game played between 2 players

I need to design the classes of a game(simplified version mentioned here) played between 2 players. Game consists of multiple rounds between the 2 players.

I have come up with 3 classes: Game, Player, Round. Game consists of the 2 players. When the round is to be started, Round object is created on the fly and players are passed to round class from Game class.

class Game
{
    Player _player1;
    Player _player2;
    int _maxRounds;
    public Game(int maxRounds)
    {
        _player1 = new Player() { Name = "A" };
        _player2 = new Player() { Name = "B" };
        _maxRounds = maxRounds;
    }

    public void Play()
    {
        for (int i = 1; i <= _maxRounds; i++)
        {
            var round = new Round(i);
            round.StartRound(_player1, _player2);
        }            
    }
}

class Player
{
    public string Name { get; set; }
    public int Score { get; set; }

    public void PlayAgainst(Player player)
    {
        //GameLogic that updates Score property of the current player
    }
}

class Round
{
    private int _roundCount;
    public Round(int roundCount)
    {
        _roundCount = roundCount;
    }
    public void StartRound(Player player1, Player player2)
    {
        player1.PlayAgainst(player2);
    }
}

Is this design correct? Should the players be part of the Round class instead of Game class? Game includes the Rounds and Players, but the Round also include Players.