All rivalries involve a dyadic relationship between two states characterized by repeated hostile interactions, whereby previous interactions affect each subsequent interaction (Goertz and Diehl 1992). Each time a state interacts with its rival, a state must choose one of two options: escalation or de-escalation of the rivalry. All possible decisions fall into one of these two categories. While it is also logical to account for situations in which a rival may choose to maintain the status quo choice, maintaining the status quo is by definition defaulting to a previous choice to escalate or de-escalate a conflict, because in either case maintaining parity requires that a state increase or decrease its level of exertion.
Prior to determining a course of action, a state must evaluate potential outcomes. The decision making process occurs in two parts: A state will first frame its decision, then evaluate potential gains and losses (Kahneman and Tversky 1979). Several factors affect the way states value potential gains and losses at each interaction. Among these are socio-cultural factors such as regime types or cultural attitudes towards violence, and systemic factors like the balance of power or the presence of outside threats. All of these factors contribute to the way states frame their circumstances which, in turn, shape the way a state values gains and losses. However, the primary drivers in the process of decision making are the economic, material, and military resources with the social capital available to a state. First, in order to escalate a conflict, a state must exert itself by expending resources. This makes the requirement for resources constant across all states, unlike socio-cultural factors which may vary from region to region and state to state. Second, while the factors that make up a state’s base of resources are not finite, they usually increase gradually. For example, global gross domestic product (GDP) grew at an average rate of 2.4 percent over the five year period between 2005 and 2009, and global population grew at an average rate of one percent per year in the same five year period (World Bank 2011).
The effect of a requirement to expend resources to escalate a conflict and the near static nature of resources cause gains and losses not to be perceived in accordance with their actual material value. This disparity between material value and perceived value is the result of states evaluating their gains and losses in terms of what the state currently possesses. In order to escalate a conflict, states must exert themselves by expending a variety of resources. The expenditure of these resources constitutes a loss to the state that expends them. For example, once ordnance is expended, it cannot be recouped; once lives are lost, those same lives cannot be replaced; and once the good will of the people has been exhausted, it takes time to recover. The American shells fired during the Korean War cannot be recouped, the lives of German soldiers lost in the Second World War cannot be regained, and the trust of the American in government lost during Vietnam could not be instantly replenished. Not only can resources not be recovered, but if they are spent on escalating a conflict, they cannot be reallocated to other programs, such as social welfare programs or maintenance of infrastructure.
In order to escalate a conflict, a state must incrementally expend more resources. The material value of the losses incurred as the result of this fixed cost increases in a linear fashion, steadily accumulating over time. Refer to Figure 1. The perception of a state’s losses, as the result of these expenditures, increases proportionally, however, in comparison to a state’s remaining capacity. Therefore, the perceived cost of escalation increases in a non-linear fashion, because the reference point from which a state views its potential losses is constantly in flux as the result of the losses from previous interactions. This trend is displayed in Figure 2.
This process can be illustrated in simple terms. If an individual has only $100 and the person spends $10 to purchase a certain good, that individual will only have $90 remaining. Therefore, the next time this individual goes to purchase the same good for the same $10, he or she is expending proportionally more of his or her total worth. In this case, the first time the individual spends the $10 on a good, he is spending 10 percent of his worth, but the second time he or she expends the $10 on the same good, he or she is expending 11.1 percent of his/her total worth. If the individual continues to purchase this same good repeatedly, the perception of how much is being spent increases as the amount of money the individual has left decreases. After five iterations, the amount of perceived loss for the same expenditure has doubled.
As a state escalates a rivalry, thus devoting more resources to the conflict, the amount of loss that a state perceives should increase at a much faster rate than the actual loss. This means that periods of continual or rapid escalation should lead directly to a decision by the parties involved to de-escalate the conflict as the amount of perceived loss begins to increase at a greater rate. For example, during the Cold War, the period of detente that began in 1969 is preceded by a five-year period during which U.S. military expenditures grew as a percentage of gross domestic product (Higgs, 1988; World Bank, 2011). Similarly, in the ten-year period before the end of the Cold War in 1989, U.S. military expenditures as a percentage of GDP grew from 5.3 percent to 7.7 percent (Higgs 1988; World Bank 2011).
In much the same way, states value gains relative to what they are currently. As a state accumulates gains, the material value of these gains increases at a constant rate. This rate accumulates slowly over time, in a linear fashion. Refer to Figure 3. When this steady increase in material gains is coupled with the need to consistently expend the same amount to receive a fixed amount of gain, the perception of the amount being gained does not increase in linear manner. As the amount of accumulated perceived gains increases, states become less willing to exert themselves because the same level of exertion yields proportionally fewer rewards when compared to the amount of previously made gains. This occurs as the result of a continually changing reference point. This effect is commonly referred to as diminishing returns, which more accurately represents how gains are perceived in Figure 4.
The diminishing effect of gains can be explained in simple terms with a mental exercise. Imagine that you have just $100. You see a briefcase with $1000 at the top of a tall rope. In order to retrieve the $1000 you must climb 25 meters up the rope to retrieve the briefcase. In this situation, most people would at least attempt to retrieve the briefcase because it offers a chance to increase your net worth by a factor of almost 10 times. Now imagine the same scenario, except in this version instead of having only $100 you have $1 billion. Is it still worth climbing the rope to retrieve the briefcase? The reward is now much less when compared to your net worth, and you stand to gain much less proportionally from the same amount of exertion.
An example of this can be seen in the U.S.-Mexico rivalry, which lasted from 1836 to 1893. Between 1846 and 1848, as the result of the Mexican-American War, the United States achieved substantial rewards. The United States gained control of territory that is now California, Nevada, Utah, New Mexico, Texas, parts of Colorado, Wyoming, Kansas, and Oklahoma. The United States could have continued to press forward and conquer large swaths of territory. In fact, the U.S. had already gained control of several key seaports and had troops in Mexico City. The country chose, however, not to escalate the conflict further. The potential gains earned from further exertion were comparatively smaller in proportion to the gains the United States had already made.
One primary criticism of this conceptualization of how gains are valued is that if a state receives repeated gains that result from the same level of exertion, a state will be willing to focus more effort on the conflict. There are two relevant situations to consider. First, there might be a windfall situation in which a sudden or rapid gain results from a constant level of exertion. Second, there might be a situation in which a constant level of exertion is met with an increasing amount of gains. Windfall situations tend to be the result of random events, such as a sudden, unexpected breakthrough that allows an army in the field to capture a large amount of territory. In the case of windfalls, the gain is fleeting. While it may encourage short-term willingness to focus more energy on a conflict, eventually gains will normalize, resulting in the continuation of a trend of diminishing returns. For example, during the Franco-Prussian war during the siege of Metz, the entirety of the French army was forced to surrender (Fortescue 2000). This windfall would have encouraged Prussian forces to continue fighting, despite the fact that prior to that point the French and Prussian militaries had lost a relatively equal number of soldiers. In both cases, however, the gains are constrained losses, which will increase at a greater rate as effort is expended, eventually overtaking any perceived gains.
When states are interlocked in a rivalry, they evaluate gains and losses in terms of their rival. A state will quantify its gains not only in terms of what it gains, but in terms of what their rival loses. At the same time, it will evaluate its losses in terms of what it loses, but also in terms of what its rival gains. By judging these two gains and losses simultaneously, a state determines the factors that contribute to whether or not it will continue to escalate a conflict. A state will continue to escalate a conflict in situations where the perceived gains exceed the perceived losses and cease escalating the conflict when perceived losses overcome perceived gains. This interaction between gains and losses is depicted in Figure 5.
Because the pain of perceived losses increases proportionally to a state’s amount of remaining resources, the faster the rate at which a rivalry escalates, the faster the amount of perceived losses accumulates. If the amount of perceived losses increases rapidly, the shorter the duration of the rivalry should become. This should occur as the pain from the perceived loss increases, and the amount of perceived gains begins to diminish, so states will become less willing to exert themselves to escalate the rivalry. If the rivalry escalates quickly in its initial stages, the amount of perceived losses will accumulate quickly. Thus, rapid escalation in the initial years of a rivalry should lead directly to shorter duration of the rivalry. This leads to our primary hypothesis: Rivalries with higher levels of severity in their initial years will have shorter durations.
In addition to the effect of initial severity on rivalry duration, we would also expect to see that as the severity of the overall rivalry increases, the duration of the rivalry should decrease. While a situation may not have a high level of initial severity, if the overall level of severity of the rivalry increases as the rivalry continues and rivals spend more on escalating the conflict, the amount of perceived losses will increase more rapidly. As losses begin to accumulate more rapidly, rivals should be less willing to continue to escalate the rivalry and more inclined to end the rivalry to prevent potential future losses, as the result of further escalation. In contrast, if the severity of the rivalry drops over time, losses will accumulate more slowly, drawing out the conflict. This brings us to our second hypothesis: As the average severity of a rivalry increases, the probability that a rivalry will terminate increases.