Zero-sum game with different payoff matrix?

Question

In zero-sum games, can we consider a situation where the players have different information (say asymmetric information)? This will result in a different payoff matrix for each player (with different entries) which means, the Nash Equilibrium would be different from each player's perspective. I do not know how to discuss the Nash equilibrium of the game? should I simply say there is two NE (for a two-person game) and that's all? Or I can find a unique NE that both players with different payoff matrices agree on that?