“The state is not ‘abolished,’ ” Friedrich Engels insisted back in 1878. “It withers away.”

Engels was mistaken about a lot of things, but he may have got this one right. For 5,000 years, states have been the most powerful organizations on earth, but they are now being challenged from every direction. Governments that go to war without United Nations resolutions are branded criminals; states that ignore the bond markets or George Soros go bust; and regardless of what they do, politicians are named and shamed by WikiLeaks.

We could all use a roadmap to this complicated new world. Now, thanks, to two insightful, readable and very different books, we are almost spoiled for choice.

Parag Khanna, a 30-something journalist and rising star in the world of think tanks, makes the case in “How to Run the World” for what he calls “Generation Y geopolitics.” He describes the 21st century as “neo-medieval,” because now, as in the Middle Ages, “rising powers, multinational corporations, powerful families, humanitarians, religious radicals, universities and mercenaries are all part of the diplomatic landscape.” Because states no longer matter much, he says, we should dump old-style diplomacy, with its “stiff waltz of rituals and protocols among states alone,” for “mega-diplomacy . . . a jazzy dance among coalitions of ministries, companies, churches, foundations, universities, activists, and other willful, enterprising individuals who cooperate to achieve specific goals.” “Generation Y,” he promises, “will own mega-diplomacy.” The result will be a new renaissance, like the one that ended the original Middle Ages.

Joseph S. Nye, by contrast, is a 70-something professor at Harvard and former dean of its Kennedy School of Government. As he sees it in “The Future of Power,” the old, stiff waltz is not over yet. “Today,” he suggests, “power in the world . . . resembles a complex three-dimensional chess game.” On the top of the board is military power, where states still reign supreme; in the middle is economic power, where states and non-state actors share the play; and only on the bottom do we find something like Khanna’s Generation Y geopolitics.

In a series of earlier books, Nye drew a massively influential contrast between “hard power” (being able to coerce others) and “soft power” (being able to co-opt others). Real power, he insists, has to be “ ‘smart power’ . . . the combining of hard and soft power into successful strategies.” His latest book is written to clarify these distinctions for critics (including perhaps Khanna, who dismisses soft and smart power as “vague concepts”) and to explain what they mean for the United States in the 2010s.

Nye recognizes that “on an increasing number of issues in the 21st century, war is not the ultimate arbiter” and that “outcomes are shaped not merely by whose army wins but also by whose story wins.” But he is not ready to cede the dance floor to the NGOs, hacktivists and celebrities just yet. “Military power,” he observes, “provides a degree of security that is to order as oxygen is to breathing: little noticed until it begins to become scarce.”

Nye is surely right that “two great power shifts are occurring in this century: a power transition among states and a power diffusion away from all states to nonstate actors.”

Khanna’s case for Generation Y is always interesting but often overstated. The state has not yet withered away, and Khanna’s recurring image of the 21st century as “neo-medieval” soon becomes strained. It has its uses (Nye, in fact, makes a similar comparison at one point), but the Byzantine Empire is a very odd analogy for contemporary America; comparing gated communities in Miami with Carolingian warbands seems unhelpful; and just what it is that modern companies should be learning from medieval guilds remains obscure.

Nye’s argument is just as interesting as Khanna’s and just as rich in clever one-liners and felicitous phrases. But it is also more judicious, more carefully presented, better referenced and, in the end, more compelling. Nye is a master of his field at the height of his powers.

Both these books repay careful reading and reflection, but Nye’s three-dimensional chess game is the better model for a world in which the state withers but refuses to go away.

Ian Morris teaches at Stanford University and is the author of “Why the West Rules — For Now: The Patterns of History, and What they Reveal About the Future.”

HOW TO RUN THE WORLD

Charting a Course to the Next Renaissance

By Parag Khanna

Random House. 256 pp. $26

THE FUTURE OF POWER

By Joseph S. Nye, Jr.

PublicAffairs.

300 pp. $27.99