[apoverton]

This is also an example of a repeated game, so over time if they maintained their strategies, investor B would own the whole company.

Also depending on how the company operates, there is another element of game theory because the controlling shareholder could elect to cancel all future dividends. if you're the newly minted majority shareholder, it's probably in your favor to do this immediately. In that case, the Nash equilibrium seems to be both parties choosing the stock dividend (and effectively getting nothing).

While the 2 shareholder example is an oversimplification in this example, after enough plays of the game (i.e. dividends) a large shareholder could take control of the company if the other shareholders always choose cash.