Why do countries that are considered world powers research, develop, and maintain nuclear arsenals despite the major risks associated with owning nuclear weapons? Major powers research, develop, and maintain nuclear weapons because it is the best way to prevent their own country being involved in a nuclear war. This is somewhat counterintuitive but can be explained through the lense of game theory using multiple games and the associated payoffs. According to Melese and Palmore, a states administration is trying to “Minimize overall risk to their nation at the lowest cost.”¹ The best real world example of how these payoffs work is to look back at the cold war between the Soviet Union(USSR) and the United States of America (USA). The Prisoner’s Dilemma, Chicken, and Stag Hunt can show how the world could have seen its first nuclear war and also why it did not.
The payoffs for the Prisoner’s Dilemma applied to the cold war between the USSR and the USA. As indicated by the numbers, the Nash equilibrium for this game is for both countries to ‘Nuke’ the other as ‘Nuke’ is the dominant strategy for both. As history shows, this did not happens. There are many possibilities as to why the cold war never turned nuclear. One is the concept of Mutually Assured Destruction(MAD) which James postulates that “[n]either state would escalate a crisis to nuclear levels for fear of second strike annihilation”.² This leads to another determining factor. This game was not just played a single time, it was repeated countless times over multiple decades and as such most likely changed the strategy implemented by both countries. Because both countries were aware of the repeated nature of the game, they understood ‘winning’ once may harm themselves more in the long run. The payoff matrix can therefore be changed to reflect the repeated nature of the game, as shown below.
Being aware of the other countries capability to retaliate changes the Nash equilibrium from nuclear war to what actually happened during the cold war. The strategy both countries end up playing in this scenario is the Tit-for-Tat strategy. According to Miller Tit-for-Tat is the most effective and the least complicated strategy for a repeated prisoner’s dilemma.³ Both countries decide to ‘wait’ until they are attacked and if they are attacked play ‘Nuke’ the next iteration of the game as retaliation. The repeated prisoner’s dilemma is a good explanation of the cold war because it reflects what actually happened during the cold war. It also explains the USSR and USA’s production of nuclear weapons as a deterrent. If only one of the countries had nuclear weapons, they would have had little hesitation launching a nuclear attack against the other similar to what happened during World War 2 when the USA dropped nuclear devices on Japan. While the repeated prisoner’s dilemma is a good explanation of the cold war, it may not be the best or only one, as changing the payoffs can change what game the countries were playing.
According to McAdams, “there is a world of value in games other than the Prisoners’[sic] Dilemma.”⁴ As reflected in the matrix above, a slight change in payoffs can completely alter what game was being played during the cold war. The new matrix now reflects a game of chicken between the USSR and the USA during the cold war. In this scenario both countries want to win but are more afraid of an all out nuclear war between their respective countries. This leads to two equal but opposite Nash equilibriums where one country attacks and the other does not. As known from history this also did not happen during the cold war and there are many possible reasons why it did not. One possibility is that both countries were playing this game and believed they had an equal chance of being the attacker or being attacked so they both chose the safe option of ‘Wait’. The other scenario is that once again the game they were playing was not a one-shot game, it was a repeated game and so their strategies may have been different. As shown below the payoffs in a repeated game will change.
The new payoffs reflect the fact that both countries want to avoid an all out nuclear war. This leads to the Nash equilibrium of ‘wait’ ‘wait’. However despite this equilibrium both countries must maintain there stockpile of weapons as they need to keep the threat of retaliation believable. While the game of chicken is not as good of an explanation of the cold war using game theory as the prisoner’s dilemma; It is still useful because the 2 countries payoffs might not reflect the prisoner’s dilemma or may have changed over time during the cold war. Another change in payoffs can once again change what game was being played during the cold war.
As shown in the above matrix are the payoffs for the game Stag Hunt applied to the cold war between the USSR and the USA. As indicated by the numbers, the Nash equilibrium for a one-shot version of Stag Hunt is what actually happened during the cold war. Both countries chose to ‘wait’ because it is their best move as long as the other country does not ‘Nuke’. This one shot game can also be extrapolated into a repeated version. The payoffs don’t change nor does the Nash equilibrium. The Nash equilibrium remains ‘wait’ ‘wait’ because both countries want to avoid being attacked by nuclear weapons. In this Stag Hunt equilibrium it is implicit that both countries should be able to disarm their nuclear weapons, however that was not the case during the cold war. One possible reason for this lack of disarmament is the need for assurance. As stated by Melese and Palmore, the USA and USSR were “both suspicious and uncertain of the other’s motives.”⁵. For both countries keeping their nuclear weapons armed and ready to deploy was a reasonable way to assure the other country that they would retaliate if attacked. This is the main reason why the USSR and USA kept making nuclear weapons throughout the cold war without ever using one in an attack.
As explained in the 3 games outlined in this paper, it is in a country’s best interest to research develop, and and maintain nuclear weapons without ever using them. The repeated prisoner’s dilemma shows this by reasoning that if the USSR or USA did not have nuclear weapons during the cold war, the other power would have attacked with impunity because they would not fear retaliation. The nuclear country would win the cold war and become a single world power. This is a major reason why the USSR and the USA participated in a nuclear arms race. The major reason for creating weapons was deterrence however if one country made a weapon that made a retaliatory strike impossible they would win the cold war and become a single world power. The weapons both countries built never became that destructive but they still were used as a major deterrent. The repeated game of chicken also shows this need to have a stockpile of nuclear weapons. Once again if one country did not have nuclear weapons they could be attacked without fear of retaliation. This created an incentive to produce nuclear weapons as a way of protecting your country. There is also an incentive to create a weapon that allows you to attack without the possibility of a successful revenge strike thereby changing your odds of winning from fifty-percent to one-hundred-percent allowing your country to attack without fear. The final game, Stag Hunt, has payoffs that actually have an allowance for nuclear disarmament. However history shows that neither the USSR or the USA did end up disarming their nuclear weapons. This could be an argument for why Stag Hunt is not the right game to apply to the cold war, however another option is to look at what game theory leaves out of the analysis. This leads to the major drawbacks of game theoretical analysis.
Some major drawbacks of this paper and game theoretical analysis in general that should be considered for further study is what payoffs are the correct payoffs. As this paper illustrates, changing the payoffs for the same scenario can completely change the game. This change in payoffs can change both the strategies of the respective players and therefore the outcome of the game. Another major factor not considered in this paper that should be studied further is how each country viewed the others citizens. One reason for not sending a nuclear attack to another country is the amount of innocent people you will kill and also how radioactive fallout will affect that countries population years into the future. Game theory does a disservice to this human factor because it removes it completely from the game. It views a country as a single player, when in reality it is one or a few leaders playing the game that may or may not take the human factor into account.
Despite the many drawbacks of this paper and game theoretical analysis, game theory does a reasonable job at explaining the cold war and nuclear weapons arming in general. Nuclear weapons are researched, developed, and maintained by major powers despite the risks because it is a good way to avoid being the victim of a nuclear attack.
