The Effect of Nuclear Weapons on International Security: Part One of Two
This essay will seek to apply the advances in thinking, made possible by rational models, to the problem of nuclear security.
∏ Mordor (swerve) = (θGondor) ▪ (0) + (1-θGondor) ▪ (5)
= (θGondor) ▪ (-2000000) + (1 – θSGondor) ▪ (100) = ∏ Gondor (Continue)
wth θ = 1/(1-X) whereas X is the cost of collision (-2000000000000)
As θMordor and θMordor are considered to be equal, as their preferences are considered equal we can say that:
θ= 1/(1-(-2000000000000) = 0,00000000049999999975%
Therefore the probability of a collision course is:
0,00000000049999999975 X 0,00000000049999999975 = 0.00000000000000000025
with a likelihood of a non-collision outcome given as
1-0.00000000000000000025 or 0.9999999999999999975
with θ as probability and pi as expected utility
So, what we can derive from this model is that, given that the cost of nuclear war remains so amazingly high, the chances of it occurring, if two rational players are given the opportunity to play, are amazingly low. In fact so low that they can roughly be equated to nothing. Although the figures used are clearly only estimates of possible damage, it is clear that the expected utility of a player is always going to be maximised by avoiding the nuclear conflict, and this will lead to a greater tendency to compromise between nuclear powers.
The next game will attempt to derive a model showing why states might try and develop nuclear weapons developed from a model used to analyse companies considering entering a market. It will attempt to explain why they do so despite the considerable pressure from the international community not to do so, and the possible perks of going along with the international community; such as aid, recognition, support and admission to the international community. Effectively this model assumes that nuclear states form a kind of monopoly of nuclear power and the authority, recognition and stability that holding such weapons provides. It also assumes that the level of utility states acquire from being part of this ’nuclear club’ is inversely proportional to the numbers of states within the club. This stands to reason, as being the sole nuclear power offers a state the effective ability to militarily dominate any other state and its allies. Whereas, as soon as two states become nuclear powers the power of the first is limited in regards to the second state, its allies and interests. So, here we derive our first assumption which is that nuclear states would rather that non-nuclear states should not become nuclear powers. We therefore assume that they would,ceteris paribus, put in effort equal to or less than the effort of keeping a state out of the nuclear circle, than they lose by letting them in. Or formally:
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