Understanding the Nuclear Arms Race — and Nuclear Nonuse — for the Past 77 Years
In the scope of international relations, the nuclear bomb has remained the most powerful weapon to ever exist in human history—yet it has only ever been used twice, during the 1945 bombings of Hiroshima and Nagasaki. Since then, world powers have only continued to manufacture nuclear weapons, with nine countries possessing roughly 12,700 warheads as of early 2022 (1). Considering this rapid increase in nuclear capability (the global nuclear arms race), the question begs—why has the nuclear bomb only ever been used twice, 77 years ago, when countries continued to develop nuclear bombs at a rapid pace? Considering game theory and Nash equilibrium, the arms race and nuclear nonuse can best be explained by the Prisoner’s Dilemma.
Arms Race (Figure 1): The use of nuclear bombs in Hiroshima and Nagasaki showed the world the capability that the U.S. had—and what type of weapon technology was possible—sending the world into an global nuclear arms race that has been going on for the past 77 years. Setting up a Prisoner’s Dilemma 2 x 2 in Figure 1, Country A’s best response is arms development, since its payoff of 1 is greater than than the disarmament payoff of 0. The same logic applies to Country B, resulting in the Nash equilibrium of (1, 1), or an arms race, rather than the disarmament value of (0, 0). The best response for both countries is arms development, explaining the rapid development of nuclear warheads since 1945.
Nuclear Nonuse (Figure 2): Considering the large presence of nuclear warheads, why have the only uses been limited to 1945? Setting up another Prisoner’s Dilemma 2 x 2 in Figure 2, both countries have the option of nuclear use or nonuse. However, this Prisoner’s Dilemma game is iterated—both countries know they will be repeating the game over and over again, as time passes in international relations. This means that the payoffs of (4, 2) and (2, 4) would never really be possible, as both countries know that if they bomb the other, they will certainly be bombed in retaliation (considering that so many nuclear warheads exist). This leaves two payoffs remaining: (3, 3), or a compromise of nonuse, or (1, 1), mutually assured destruction. Knowing that the game is iterated, the best strategy for both countries is to always cooperate, since the payoff (3, 3) is higher than (1, 1). Both countries can also count on the other to always cooperate, since they know the other would prefer the higher payoff (3, 3) over (1, 1). This explains why no country has used the nuclear bomb since the 1945—the fear of mutually assured destruction.
Effectively, these two Prisoner’s Dilemma games explain the global nuclear arms race and nuclear nonuse policies for the past 77 years.
(1) https://fas.org/issues/nuclear-weapons/status-world-nuclear-forces/
(2) https://doi.org/10.1177/0022002789033001003