One of the contemporary issues in international relations is that the current hegemon, the United States, has undergone a relative decline. It is argued that American hegemony that emerged aftermath the Second World War is undergoing a decline and with the rise of a potential challenger in China looming, one major issue concerning IR scholars is whether or not the relative decline of US hegemony will result in a hegemonic war.
Hegemonic wars occur when a rising challenger – revisionist power – isn’t content with the current international order and wants to change it so as to become a preponderant force and dictate terms of a new world order. This article assumes that although the US is in a relative decline it is still a dominant power and the rising power is content with the current status quo so no war occurs between the dominant and the rising power. In order to support the argument that a hegemonic war does not occur, this article provides explanation using several theoretical perspectives.
Structural Realism and Balance of Power
To begin with, prominent neorealist Kenneth Waltz contends that the end of the Cold War has changed the structure of international politics from bipolar to unipolar with the US being the dominant power. According to Waltz, days of US being unipolar force in world politics is numbered and slowly the world is moving towards bipolarity or multipolarity because changes in the structure of international system brings about changes in state behavior. It does not matter how much self-restraint and self-control a preponderant power is in its conduct of international relations; states are always wary and fear the dominant power and thus he maintains that balancing is universal. 
In order to explain why, he has resorted to the Balance of Power (theory). In most basic sense, international politics is a state of anarchy where there is no central government and states rely on themselves to protect their autonomy and perpetuate their survival. Balance of Power contends that states involve in a balancing act to check the powers of preponderant force so that no any single state has enough power to become a global hegemon. 
With the relative decline of US, China and America can enter into bipolar relationship much like the US and the USSR during the Cold War. Since Waltz himself posits bipolarity as the most stable of international configurations, it can be argued that act of balancing between the US and China brings the international distribution of power into an equilibrium and averts the risk of war.
Socialization of Hegemonic Power
Most scholars posit that hegemons use threats and rewards to get compliance from secondary states. Contrary to popular wisdom, scholars Ikenberry and Kupchan have contended that in addition to material power, hegemons also have the power of socialization to achieve compliance from secondary states. They call this the socialization process which involves ‘altering of the belief systems’ of elites.
Basically, hegemons project their vision of international order through normative principles (norms and values) and not by material incentives; elites in secondary states internalize them, and devise policies that are compatible to the hegemon’s ideal of the international order. The authors contend that the world order thus created can sustain even when hegemon undergoes a decline because the world order created is relatively inexpensive to maintain in the sense that altering of states preferences are by virtue of ideals rather than use of coercion. Thus, by virtue of socialization of hegemonic power, relative changes in hegemon’s distribution of material power (military and economy) does not put strain on the international system.
So, on viewing the world from the lens of socialization, it can be argued that the expansion of US normative principles on liberal economic norm to its former allies and enemies aftermath the second world war that led to the formation of the current liberal economic world order provides an explanation as to why in spite of US’ relative decline there is continuity for America’s liberal economic order.  The rising challenger China can be considered to have been socialized – it has accepted US led international norms, and participates in various International Organizations. Thus, it makes less sense for China to wage war against the hegemon whose ideals it has internalized.
Hegemonic Stability Theory
According to this theory, a hegemon creates a stable international economic order characterized by market openness but its decline results in global instability. This hegemonic effect of open trade benefits all participants, especially, weaker states that do not have any burden of public goods. In this sense, global economic stability is born out of hegemony and provides provision of collective public goods and in doing so facilitates a stable international system.
The motivation to create an economic openness lie in the interest of the hegemon – it has the largest economy and so benefits most from open markets. In addition, only hegemons have the material capability (political and military) to provide public goods and induce other states to embrace open trade. 
By virtue of the Hegemonic Stability Theory, the hegemon is an important element in creation and maintenance of the international system. As stated earlier, open trade benefits all participants, even the rising challengers that are accommodated in the system. In contemporary world politics, China is the fastest rising power and it is also reaping the benefits of the open economic order created by the US. By participating in the globalized economy, China has earned a comparative advantage in labor-market and its economy has been growing. On top of that China is an export-based economy and thus, it has very little incentive to jeopardize this benefit by engaging with the hegemon and thereby disrupting the order. In his article, Artur Stein has argued that decline in hegemony does not bring about a complete collapse of the trade regime as long as hegemonic power is committed to economic openness. Taking these two points in consideration, it can be argued that it is not in the interest of China to challenge US hegemony. On account, likelihood of war is averted. 
Robert Keohane and Institutionalist Approach
In After Hegemony, Robert Keohane uses an institutional approach to explain inter-state cooperation. He posits that states have common interest and in order to realize it requires achieving mutually beneficial agreements which is where international regimes come in. These regimes foster cooperation by making it easier to reach mutually beneficial inter-state agreements. They help overcome the problem of lack of qualitative and asymmetrical information, through institutional embeddedness reduces transaction costs, legal costs reduce incentive to cheat thereby reducing uncertainty and building confidence among states. Since hegemonic leadership is required to create regimes in the first place, even after the erosion of hegemony, they have high stakes and play important role in fostering cooperation (US role in the IMF and WTO). Because cooperation fosters absolute gain, all participants are benefitted.  By this approach, states see cooperation more beneficial than conflict. Thus, it can be argued from institutionalist approach that international regimes foster cooperation thereby reducing likelihood of conflict in the event of hegemonic decline.
The article provided four distinct perspectives with regards to declining US hegemony and potential of a hegemonic war. Using these approaches the article concludes that in spite of decline in American hegemony there will not be a significant change in the current structure of the international system mainly due to power differentials between the US and its nearest challenger China. The US is undergoing a relative decline but still, it is the largest economy boasts strongest military and has highest political leverage. In sum, prospect of a hegemonic war in contemporary world politics is only a far-fetched dream.
 Waltz, Kenneth N. “Structural Realism after the Cold War.” International Security 25, no. 1 (2000): 5–41. https://doi.org/10.1162/016228800560372.
 Baylis, John, Steve Smith, and Patricia Owens. The Globalization of World Politics an Introduction to International Relations. Oxford: Oxford University Press, 2014.
 Ikenberry, G. John, and Charles A. Kupchan. “Socialization and Hegemonic Power.” International Organization 44, no. 3 (1990): 283–315. https://doi.org/10.1017/s002081830003530x
 Snidal, D. (1985). The limits of hegemonic stability theory. International organization, 579-614.
 Stein, Arthur A. “The hegemon’s dilemma: Great Britain, the United States, and the international economic order.” International organization 38, no. 2 (1984): 355-386.
 Keohane, R. O. (2005). After hegemony: Cooperation and discord in the world political economy. Princeton university press.