The Effect of Nuclear Weapons on International Security: Part One of Two

In figure 1.4 we have amended the basic model to add a move by ’nature’ which is observed by player one, but not player two.  In effect this move by nature determines the relative power of the state that we are talking about.  In this context, by a ‘strong’ state we are referring to a state that has the resources,  commitment and stability to participate in a lengthy confrontation that may well involve diplomatic and economic sanctions. So, we might say that Iran, with its high oil revenues relatively stable state system and commitment to self defence is a strong state as it could resist sanctions over a prolonged period of time.  Given these criteria, it is clear that fighting with a strong state would be irrational for  the hegemonic power, giving a payoff of 0, and thus collusion would ensue.  However, if the incoming state is a weak state, the payoff if set at ’X' for state B, if this figure is greater than 90 and the hegemonic power knew that the state was weak, then they would commit to the fight.  Importantly, in our game the hegemonic power is unaware if the state is a strong state or a weak state, thus is only able to infer which it is through its actions.  So, if the state enters the nuclear race, the hegemonic power is forced to assume that it is indeed a strong state, and thus collude, even if they might benefit from the fight if the state were weak.  This creates a dominant strategy for the first state, to simply develop nuclear weapons, regardless of its power.  This represents a Bayesian equilibrium, where the players update their strategy based upon information inferred from the actions of other players. 

Looking again to figure 1.4 , if we now amend ’X' to 60 we find that if the state is a weak state it is of benefit to the incumbent hegemonic power to start a conflict while the entering state is weak.  If we assume arbitrarily that the probability of a state being weak is 50%(passive conjecture).  Then we now look at the expected utility of different stratagem we can see what the probable equilibrium is.  If we look at the dominant strategy of the hegemonic incumbent; we can see that the move of ‘conflict’  produces an expected utility of 30, as there is a fifty percent chance of the entrant being a strong state resulting with a pay-off of zero, and a fifty percent chance of the entrant being a weak state resulting in a pay-off of sixty, giving the thirty expect utility.  Giving that this is less than the expected utility of collusion, the entering state will choose to enter.  Importantly though, if we were to change the probability that a state was a weak state to 0.9, the expected utility would modify to mean that conflict would be the expected strategy of the incumbent hegemonic power, and therefore given that information the first state would choose not to develop nuclear weapons.

Figure 1.5 adds in another move by nature that might affect the way the game works.  In this game the probability that the entering state would use the nuclear weapons, once acquired, to commence a  nuclear conflict is added in by another move by nature, which offers a probability of the state being prone to nuclear conflict.  This is of particular importance when it comes to our later discussions on Iran and nuclear proliferation, as the perception of the likelihood that Iran would use its nuclear weapons would change the pay-off structure of our game, thus altering the incumbent hegemonic state’s strategy.

We have seen how our rationalist model can be developed into ’games’ that allow us to predict the actions of ’players’given certain criteria.  However, as we have made clear, arbitrary changes in our exogenously derived preferences affect the probable outcome.  Thus we must be extremely careful not to overestimate the predictive quality of our games, as they are only as strong as the assumptions used and the utility levels assumed.  This essay will now examine how plausible it is to assume levels of utility that are broadly homogeneous, and a consistent rationality of players.