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The term arms race can be used to describe any competitive situation where the goal of each competitor is to stay ahead of the others. The phrase came into common parlance in descriptions of the causes of World War I, where it has been suggested that the major European protagonists—Austria-Hungary, France, Germany, Russia, and the United Kingdom—increased their armed forces to match what they saw their rivals doing. It has been argued that the massive increase in those forces and the tensions between the states over trade and empire inevitably led to war.

In more recent times, during the cold war, a nuclear arms race developed between the two superpowers—the United States and the Soviet Union—as each eyed the other's nuclear weapons, and both increased their first-strike capabilities. Similar arms races with both conventional and nuclear weapons can be seen in different parts of the world: between India and Pakistan, between Israel and Arab nations in the Middle East, between North and South Korea, and at various times between neighboring African and South American countries.

Lewis F. Richardson mathematically modeled arms races. He suggested three motives led nations in peacetime to increase or decrease their armaments. First, revenge or hostility to another nation; second, fear; and third, working in the opposite direction to reduce weapons to economize. Tension and past hostility obviously increase the probability of an arms race. Richardson's work has been studied extensively by mathematicians, economists, and others and applied to arms races between nations and to firms in competitive markets.

The term arms race is now also extensively used in evolutionary contexts to describe the dynamic evolution of aspects of plants and animals. For any two species that compete in a given environment, any improvement in one species will lead it to have an evolutionary advantage over its rival. Thus, if the rival species is not to decline to extinction, it must also improve in some respect. Thus, two different grass-grazing animals must each increase their ability to drive off the other from scarce grassland. The prey must match an increase in the speed or agility of a predator. Over time, a species might lose some of the features that made it more competitive: it might become less agile, but expend its resources on other features, perhaps stronger bones or warmer coats, that advantage it in other ways. The evolution of reproduction is an important consequence of arms races and enables species to evolve more swiftly. In evolutionary biology, this has been termed the red queen hypothesis, after the Red Queen's dictum (in Lewis Carroll's Through the Looking Glass) that one must keep running to stay in the same place. In evolutionary terms, this translates to finding that the probability of any species surviving over geological time remains constant (outside of major environmental changes) despite its constant improvement in its members' ability to compete. Coevolutionary processes are not arms races, but can improve “cooperating species” against other species.

The evolutionary finding can then be applied back to markets where firms must keep improving products to give themselves the same chance of surviving, and countries must keep improving their weapons to keep the same probability of winning future battles. As with coevolutionary processes, cooperation between firms can enable them to keep their market positions without improving, whereas countries might tie their futures together through trade, thus reducing the probability of future conflict and, consequently, of arms races. Thus, we can see arms races have both advantages and disadvantages.

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