This is a bit late, but here is an awesome blog from Foreign Policy applying an international relations reading to The Game/Jay-Z beef. Basically, Jay-Z is the rap version of the U.S. hegemon while The Game is a dangerous middle power on the attack. Some reasons, under an international relations narrative, that The Game is attacking now: Jay-Z's age, his overextending, the prevalent resentment among the younger generation of up and comers and middle-powers. Writer Marc Lynch not only writes a pretty airtight comparison but also gives good informed primers on the careers and beefs of both rappers.

Here's a bit on Jay-Z's position at the top and his strategic options:
"But the limits on his ability to use this power recalls the debates about U.S. primacy. Should he use this power to its fullest extent, as neo-conservatives would advise, imposing his will to reshape the world, forcing others to adapt to his values and leadership? Or should he fear a backlash against the unilateral use of power, as realists such as my colleague Steve Walt or liberals such as John Ikenberry would warn, and instead exercise self-restraint?
The changes in Jay-Z's approach over the years suggest that he recognizes the realist and liberal logic... but is sorely tempted by the neo-conservative impulse. Back when he was younger, Jay-Z was a merciless, ruthless killer in the "beefs" which define hip hop politics. He never would have gotten to the top without that. But since then he's changed his style and has instead largely chosen to stand above the fray. As Jay-Z got older and more powerful, the marginal benefits of such battles declined and the costs increased even as the number of would-be rivals escalated. Just as the U.S. attracts resentment and rhetorical anti-Americanism simply by virtue of being on top, so did Jay-Z attract a disproportionate number of attackers. "I got beefs with like a hundred children" he bragged/complained on one track."