How can information in 4-dimensions be pictured using 2-dimensional diagrams?

This question concerns how to reduce information in 4 dimensions to a representation (or set of representations) in 2 dimensions.

For background, consider the economic duopoly situation, with two firms producing non-identical products. A standard textbook way of picturing the solution is to construct “Reaction Curves” RC1 and RC2, showing each firm #1’s optimal quantity response Q1 to the other’s entire range of possible quantity choices Q2, and vice versa. The Cournot-Nash solution is at the intersection of the two Reaction Curves thus constructed, where each firm’s choice is a best response to the other’s. (The associated prices are not pictured, but are implicitly determined by the market demand function for the two products.)

Now here’s the question. Suppose the firms can vary not only quantities produced (Q1 and Q2) but also the nature of their products — measured as V1 and V2 on some numerical scale.

Instead of the previous 2-dimensional space on Q1,Q2 axes there is now a 4-dimensional space on Q1,Q2, V1,V2 axes. In this space the previous Reaction Curves now become Reaction Surfaces: firm #1 chooses a profit-maximizing (Q1,V1) vector in response to any (Q2,V2) choice on the part of its rival, and vice versa. As before, the Cournot-Nash condition will be met at the intersection, so that the firms’ choices are best responses to one another.

I believe the two Reaction Surfaces will intersect generically at a single point if all the functions are ideally well-behaved, or at any rate at a finite number of points.

But is there any way of representing this solution that would permit some intuitive glimpse of the process? I’ve been playing without success with linked pairs of 2-dimensional diagrams. For example one diagram on Q1,Q2 axes and the other on V1,V2 axes.