Why do some hostile relationships between states last for generations while others eventually give way to cooperation? International politics offers many examples of both outcomes. France and Germany moved from repeated wars to partnership, while the rivalry between India and Pakistan continues despite decades of conflict management efforts. Explaining why some enduring rivalries survive while others transform remains one of the central questions in the study of international conflict (Goertz and Diehl 1993; Diehl and Goertz 2000). Rivalries are among the most enduring features of international politics. They structure how states perceive threats, allocate military resources, form alliances, and pursue foreign policy objectives. Some rivalries endure for decades despite wars, leadership changes, and shifting international circumstances, while others gradually give way to more cooperative relationships.

The question matters because enduring rivalries have shaped some of the most consequential conflicts of the modern era. They have influenced alliance formation, military competition, arms races, territorial disputes, and patterns of regional instability (Thompson 2001; Colaresi, Rasler and Thompson 2007). Yet rivalries are not static relationships. Wars, crises, and political upheavals do not affect rivalries uniformly. Relationships that appear deeply entrenched can sometimes change quickly, whereas others endure despite repeated disruptions. Understanding why these different trajectories occur is important not only for explaining the past but also for making sense of contemporary conflicts.

Research on enduring rivalries has generated valuable insights into the causes of rivalry formation and persistence. Scholars have highlighted the importance of territorial disputes, repeated militarised conflict, power asymmetries, domestic politics, and security dilemmas (Vasquez 1993; Huth 1996; Jervis 1978; Diehl and Goertz 2000). These explanations have significantly advanced our understanding of rivalry dynamics. At the same time, much of the literature implicitly treats rivalry change as a relatively linear process, where major events are expected to produce corresponding changes in rivalry behaviour. Historical experience suggests a more uneven pattern. Similar shocks can produce sharply different outcomes across rivalries. Some rivalries persist despite events that appear transformative, while others end following a combination of developments that may seem less dramatic when considered individually.

Major shocks are often treated as turning points in rivalry histories. Historical experience, however, offers a more complicated picture. Some rivalries survive wars, territorial settlements, and systemic upheavals, while others undergo significant transformation. Understanding this variation requires looking beyond disruptive events themselves and examining the conditions that shape how rivalries respond to them. I argue that rivalry stability is best understood as a bounded range within which rivalries can absorb repeated pressures without fundamentally changing their character. At the same time, Rivalry Tipping Points (RTPs) highlight moments when those pressures may begin to generate more substantial change.

The Limits of Existing Rivalry Explanations

Research on enduring rivalries has generated several influential explanations for why hostile relationships persist over time. One of the most prominent explanations emphasises territorial disputes. Territory often carries strategic, economic, and symbolic value, making such disputes particularly difficult to resolve (Vasquez 1993; Hensel 2001). Rivalries such as India–Pakistan demonstrate how territorial issues can remain politically salient across generations, sustaining competition long after their original causes have evolved. Other scholars emphasise shifts in relative power and changes in the broader international system. From this perspective, rivalry behaviour is shaped by changes in capabilities, alliance structures, and the distribution of power among states. Rivalries may weaken or transform when these conditions alter the incentives for continued competition.

The security dilemma offers a different explanation. States attempting to increase their own security can unintentionally generate insecurity for others, producing cycles of suspicion and military competition that become difficult to reverse (Jervis 1978). Domestic politics also matter. Regime characteristics, leadership choices, and nationalist pressures can all contribute to the continuation of rivalry, even when cooperation might otherwise appear beneficial (Russett 1993). Together, these approaches have improved the understanding of why rivalries emerge and persist. Yet one important question remains unresolved. Rivalries exposed to broadly similar disruptions often experience very different outcomes. Some survive wars, territorial settlements, and major political changes, while others transform or terminate.

The contrast between the Franco–German and India–Pakistan rivalries illustrates this puzzle. Both experienced repeated wars, territorial disputes, and periods of crisis. Yet one eventually evolved into a cooperative relationship, while the other remains active. Likewise, World War I failed to terminate the Franco–German rivalry, whereas the combination of developments after 1945 contributed to a very different outcome. Existing explanations identify important influences on rivalry behaviour, but they provide less guidance on why comparable disruptions can produce such different consequences. This puzzle suggests that rivalry outcomes depend on more than major shocks alone. Equally important is the extent to which rivalries are able to absorb disruption without losing their underlying competitive character. It is this issue that motivates the Rivalry Stability Range framework developed below.

The Rivalry Stability Range Framework

One striking feature of many rivalries is their ability to survive events that appear capable of transforming them. Yet these same rivalries can sometimes transform rapidly when particular combinations of events occur. The more difficult task may be explaining why rivalries survive repeated disruption in the first place. Much of the rivalry literature has tended to treat stability as an implicit condition rather than an object of analysis in its own right. Rivalries are often classified as active or terminated, while the processes that sustain them between these outcomes receive less attention (Diehl and Goertz 2000; Thompson 2001). The framework begins from a simple observation: rivalry stability is often taken for granted, even though it requires explanation. Instead of treating stability as something states either possess or lack, the framework views it as a range within which rivalries can absorb pressure without becoming something fundamentally different. Rivalries are therefore neither........

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