Offensive-Defensive technologies model + Arms Race Model Flashcards
what is the offence/defence ratio
Attack/defence ratio: Levy points out that military technology and tactical doctrine determines the defence-offence balance by defining the minimum “attack/defence ratio” required for an attacker to overcome a defender. This ratio determines the balance, though not necessarily the outcome, since the outcome depends on both the minimum attack/defence ratio and the amount of troops available. If the basic view is that attackers need to outnumber defenders three-to-one before they have a good chance of winning, that determines the offence-defence balance.
Military conditions will require a certain ratio between the attacking forces and the defending forces in order for the attacker to succeed. The simplest model has two sides, A and B with military forces Ma and Mb. For A to attack B and win, it needs to have a military force “g” times as big as B’s. Similarly, B needs its military force to be “h” times the size of A’s in order to win in an attack.
Use this parameters to illustrate when an attack by A, or B would be successful
If Ma > gMb, A can attack B and win. If not, B can successfully defend against A.
In other words, if A has the certain multiplier g to defeat B
If Mb > hMa, B can attack A and win. If not, A can successfully defend against B.
use parameters g/h to explain when offence or defence will have the advantage and why
If g > 1 and h > 1, then in general the military technology is one that favours the defence. If g < 1 and h < 1, then offensive technologies dominate. If g is less than 1 (g<1), then A doesn’t need as many troops to defeat B so technology favours offence. If g is greater than 1 (g>1), then A needs more troops to defeat B so the technology favours defence. But remember you can have cases where g and h can be different, and you would have to represent that.
Stable nash equilbruim with a defensive advantage: Explain the graph on page, the difference sections, the zone of mutual defence, and what it would look like in the case of offensive advantage
In the diagram Ma = gMb is the equation showing when A is just capable of matching B’s defences. For areas below that line, A could successfully attack B because its military force exceeds B’s defensive capability. Just look at the graph because A would have so much more forces than B at any point below this line.
Similarly, for areas above the line Mb = hMa, B can successfully attack A. Again, look at the diagram, B would have so many forces than A, and would be able to successfully defence.
For areas where (1/g)Ma < Mb < hMa. Neither can attack successfully.
If there are areas where (1/g)Ma > Mb > hMa, then both can attack successfully.
The larger the region of defence the more area there is for stability – you know here that technology favours defence because gh>1
In effect, when conditions favour the offence, the line Mb = hMa becomes flatter and the line Ma = gMb becomes steeper; mutual defence is less likely. This is because a flat B line indicates that little troops are needed to attack, whereas, a steep A line would indicate the same. In the diagram above there is a range of relative weapons availability that leads to mutual defence; neither side has the ability to conquer the other. Only in cases of substantial weapons superiority will attack succeed.
explain the different sections of the offensive advantage model on page 4
the two lines switch positions. When forces are unbalanced, the stronger side is generally able to successfully secure its defence. The larger the area that both can attack the less stability there is. The idea is basically that look at A’s line in defence where it can successfully attack, now look at its line when offence has an advantage where it can successfully attack, the space that both sides can successfully attack increases for both sides, and the space they can defence reduces for both sides. Green area – where A can attack Orange area – where A can defence Pink area – where B can attack Red area – where B can defend Black area – where both can attack
Use parameters gxh (gh combined) to explain whether a zone of mutual offence or defence will exist, and whether war will then occur in either case
The product gh (or g x h) can then be used to define precisely what is meant by defence/offence balance. If gh > 1 then a zone of mutual defence (as in the first diagram) exists. If gh < 1then a zone of mutual attack as in figure 2 exists (which would be similar to the pre-emptive war problem because both sides have an incentive to attack). The further gh is from 1 the larger these zones are
Everything is there for war to occur, but what would cause war not to occur? If the cost of war still really high, so the first two strike points could still be in the PPF and there would still be a zone for mutual settlement, or it could be outside which there would be war. So, this doesn’t guarantee war but certainly looks less stable than mutual defence, and we still have to appeal to the other elements of rational war to be able to say that war should not emerge.
Conflict management implications in both the offence and defence models
Defensive model: Third party would support one side to bring about a balance where both can defend, and war would become less likely. Balanced forces would result in a higher likelihood in peace. Supplement the weaker side by giving them weapons for example, this would decrease the space that each side has to carry out a successful attack, and increase the space of mutual defence.
Offensive model: Bring about balance by siding on one side by convincing that it’s not worth the attack/conflict . For example, a third-party might intervene and say whoever is attacked first, I’ll side with and help defend them, so you’re essentially eliminating the offensive advantage one side might have. Also, reconfigurations of weapons technologies and military organizations away from offence to defence by one side, or placement of peacekeepers between rivals could reduce relative attack effectiveness and change an offensive model to a defensive one.
Limitations of offence/defence model: (aversion by side payments, contract space, comparison to peace and war, costs of war, fundamental problem with rationality)
The outcomes of these games are interesting, but determinate. There is no attempt to suggest that both sides, having accepted the consequences of the model, might avert war by side- payments.
They might indicate how big our contract space is.
There is no attempt to understand what is won by choosing war as an option, simply an attempt to explain what might happen militarily if war takes place. Effectively, there is no comparison of peace to war, and no incorporation of a cost of war.
Ultimately, however, it leaves unresolved the question of why the sides want to fight in the first place. This still doesn’t solve the fundamental question of rationality, there is still no incentive to go to war even though one side is a lot stronger, there is no disagreement, there is perfect information, and both sides can still do a deal on the side and avoid the costs of war. It still doesn’t tell you the reason why war would occur, indeed though it shows you where the contract space should be. It’s more or less who would win if we were at war.
What is the arms race model and what are the three factors that determine the level of arming
One important element of conflict not present in Fearon’s models is the preparation for conflict. Knowing that conflict is a possibility, groups or countries will expend resources to prepare for conflict, both to improve the chances of winning or to avoid conflict altogether. This approach leads to the traditional dictum of “if you want peace, prepare for war”, which is a staple of deterrence theory.
Rivals decide to arm themselves based on three factors:
The first is the degree of sensitivity to each others’ weapons stock. The more sensitive (or less trust, more insecure) a country is, the larger its reaction will be to its rival’s weapons policy. As rivals, the reaction is direct (and in this case for simplicity assumed to be proportional) so that when one state increases its weapons stocks, so does its rival in response.
The second characteristic is the cost of weapons acquisition. This feature of the model reflects the extent to which a country has to make economic sacrifices to acquire weapons, i.e. the opportunity cost. There may also be other costs, such as political or reputational, but the idea is the same. The tradition in economics is that as the level of production of a good increases, so too does its opportunity cost. The level of opportunity cost is related only to each player’s own level of arming.
Finally, each country is also characterized by a parameter that measures the extent of its grievance against its rival, ambition to conquer it, or other source of hostility. This factor is a given characteristics unrelated to the level of weapons in either state.
“k” (“r”) is the sensitivity of player A (B) to the arms level of its opponent, i.e. player B (A), so that if player B increases its arms level by one unit, A will respond by wanting to increase its level of arms by k times the change in B’s arms.
α and β are the opportunity costs of accumulating weapons for A and B, respectively.
The variables g and h represent the other exogenous elements of the rivalry unrelated to the level of arming, for A and B respectively; these elements could include fundamental levels of hostility, ethnic hatred, rivalry or similar dimensions of their relationship.
Explain the arms race equation on page 6
ṀA increases with the level of weapons of B (MB) by a factor k
k represents the sensitivity of A to B’s arms level - A will respond to how much weapons B acquires by a factor of its sensitivity
ṀA decreases with the cost of it own arming level MA by factor α
α is A’s arming cost factor
Finally, ṀA increases with some exogenous constant factor g, reflecting rivalry
g represents the level of arms A would choose if B had none and there were no costs to arming
What is the stable nash equilbruim mean in the arms race context, what are the reaction curves supposed to mean, and explain what would happen page 7 graph
These differential equations can be solved for what we refer to as “stationarity”, i.e. the level at which a country does not wish to change its stock of weapons.
In effect, this would be identical to the concept of a think of a Nash equilibrium. To solve for stationarity, just set each of the above equations equal to zero, indicating that there is no more desired change in arms levels.
Equilibrium occurs when ṀA = 0 and ṀB = 0 i.e. no more change. This is when the first equation above is equal to 0 and then it implies so its rearranged to the bottom equation
MA = (k/α)MB + (g/α) and MB = (r/β)MA + (h/β)
The nash equilibrium is the level both players are happy with their level of arming
•You can think of these as reaction functions:
for each level of MB there will be a preferred arming level for A
for each level of MA there will be a preferred arming level for B
If I’m player B and I’m on my line then I’m happy which is the red line, the red line represents the equation – B’s reaction function is the red line
How each sides reactionary curve would react:
In the above diagram the equilibrium at E is stable, since any shift in the military stocks would lead to a process of military stock adjustment that would end up back at E.
Any points to the right [left] of A’s reaction function suggests that for the given level of arming by player B, player A would want to have fewer [more] weapons, and they would thus reduce [increase] their weapons stock and move to the left [right].
Note, then, that when player A does not have their desired level of weaponry, they adjust the level and end up moving horizontally left or right in the direction of their reaction curve. The same logic is true for player B, except they can only adjust their level of weaponry up or down.
In other words, lets use the point to the right of E as an example; in that case, A would move left to reduce arms and B would down to reduce arms as a result of their reaction functions. They prefer disarmament in this case because of the inputs that go into their reaction functions.
This is a stable nash equilbruim – I could start off at any point and they would go back to the equilibrium
Parameter changes in the arms race model:
- what happens if more or less sensitive for each player
- what happens if cost of war goes up or down for each player
- what happens if rivalry goes up or down for each player
So the more sensitive a country is to its rival’s arms, the more it will arm in reaction;
For player B - the sensitivity parameter is captured in the slope, because I’m less sensitive that would also change – that’s captured in the new orange line. For B this would mean moving the line down.
For player A sensitivity is in both equations – lets say sensitivity goes down and the new reaction curve for player A would be the new yellow line – this again would change both the slope and the y-intercept
the higher the cost of its arming the less it will arm both in general and in response to the rival,
for player B cost is in both equations cost goes down – if beta is going down the slope becomes steeper, but beta is also at the y-intercept so the line would also change – the new purple line, not surprisingly, weapons are cheaper so the line will actually higher and steeper. That will look a little like an arms race until we get to the new equilibrium.
if cost goes up than the y-intercept and the slope should also be reflected so arming goes down
and the larger its initial ambitions or grievance, the more it will arm.
If that goes up that is captured by the intersect h which gets bigger, and B’s line would start higher – this would be the new line in the graph below – the red line. You could see a new arms race until the points keep going to the new equilibrium. So player A responds by increasing its arms to the new equilibrium because its sensitive to player B but its reaction function doesn’t move.
What if A’s sense of rivalry goes down – that’s the new green line, so the level of arms would decrease – shifting to the left and a decrease of overall arms in the new equilibrium
What happens to the two lines in an unstable nash equilibrium (cost/sensitivity & slope) and explain the arms race dynamic on page 11 graph
Unstable Nash Equilibrium Section: The two lines are now flipped, and A’s line starts above B’s, because since both sides are more sensitive then their slope changes (A becomes flatter and B becomes steeper)
Unstable nash equilbruim occurs when cost is relatively low, and sensitivity is relatively high
(k/a) (r/B) = < 1 then the players are not overly sensitive to rival military stocks and there is a stable equilibrium
(k/a) (r/B) = > 1 reflects a runaways arms race and unstable equilibrium
Both are in reference to the slope; if the slope is greater than 1, then unstable
In the example below though, the coefficients cause the slope terms to be relatively large causing each side to react strongly to the militarization of their opponent. Taken together, it is expected that B will want to move up and A will want to move the right. B’s become steep and A’s become flatter because both are more sensitive.
The new lines means that both sides have become more sensitive
B can only increase or decrease its level of arming so it would go up from the new point so it would move up by yellow, then A would react with red increasing, then B would also react with black, increasing too, and this reflects an unstable nash equilbruim with the risk of an arms race. Because there’s still an equilibrium but, when we move away from it, the situation quickly turns into an arms race.
If both players were very sensitive to their opponents, then the reaction curve for A would become flatter (k is bigger) and the reaction curve for B would be steeper (r is bigger). (Since k is bigger, A’s reaction curve would also shift up a little). In this case the lines may intersect at a stable equilibrium with much higher levels of armaments, or may not intersect at all (violating the stability condition of (k/α) (r/β) < 1; note that the stability requirement is that the slope of B’s reaction curve is less than the slope of A’s reaction curve when presented in the same diagram, i.e. (α/k) > (r/β), or (α/k) (β/r) > 1). The same outcome of inflated arming or unstable arms race may also occur if the opportunity cost of arming is very low (α and β very small).
explain the flip side of disarmament in an unstable nash equilibrium context
There’s the flip side though, if B loses some weapons and they end up at the black point, then A would respond by losing weapons with the red line, then B would also disarm. So, even though an unstable equilibrium can result in an arms race, it so too can result in disarmament.
If levels of ambition were also really low, even ‘negative’, then not only would the system be more likely to generate a stable equilibrium (A’s reaction function shifts to the left, B’s shifts down), the equilibrium would be at lower levels of arming. In the extreme you could even have a very stable equilibrium with no weapons (the disarmament ideal?) if the slopes remained as in the diagram but A’s reaction curve intersected the vertical axis above zero and B’s curve intersected the horizontal axis to the right of zero.
What is the saddle path route and explain the graph on page 13
Interestingly, with very low levels of ambition (as in 2 above) but very high levels of sensitivity (as in 1 above) there is a more bizarre unstable equilibrium possibility in which for low levels or arms there would be a tendency to have both players move to no weapons, with an unstable armed equilibrium, and a region of open arms race beyond the unstable equilibrium level. There is also going to be a unique “saddle-path” equilibrium running with a downward slope through point E, that is a unique path of A and B military stocks that are away from E that would be just balanced enough to lead to point E, an unstable equilibrium. They would be pushing in those directions simultaneously to lead back to the nash equilibrium., This is a case where you can get back to the nash equilibrium even if you’re off of it. All is not lost with an unstable equilibrium.
