Commitment Problems and Indivisibility Flashcards
Commitment Problems: Conflict due to commitment problems shows how conflict emerges even if there is no private information or incentive to misrepresent.
Solve the following below and illustrate the consequences. Why it alone is not a good explanation for war.
1. Pre-emptive war (page 15): Pre-emptive war scenarios arise when first strike advantages are great. When interpreted as a first strike leading to an increase in the probability of winning (the gunslinger problem) a commitment problem arises. Fearon analyzes the results using the same linear model as before. The logic is as follows. The first strike advantage means that the expected division favours the first mover. Let the expected division be Ef for when A is the first mover and B moves second, Em when they attack at the same time (mutual strike), and Es for A as the second mover and B attacks first. Note that on the line representing the division (think from A’s perspective) Ef > Em > Es is the numerical logic of the game. Fearon then includes costs for each player (Ca and Cb) of the war, which he assumes constant across strike scenarios in his presentation.
The best that player A can do in the game is to strike first and accept the cost of Ca, getting a total of Ef-Ca (a diminution of its share of the division from A’s perspective) if player B doesn’t strike at the same time. The best B can do is to strike first when A does not, in which case it gets Es + Cb (recalling that this represents a reduction for B from the division Es). There is no contract space: war will occur.
Fearon doubts that it is a good explanation of war, since if these conditions ever really occurred there would be little by way of communication to avoid war and we would see it much more frequently, and without linkages to other potential conflict factors. Instead Fearon suggests that under these circumstances, which may be thought of as an extreme case of the security dilemma, that it contributes to conflict by narrowing bargaining ranges where other factors are generating conflict. The main point is that even if we negotiate we can’t commit to it because one of us will be tempted to renege.
A second model of pre-emptive war (Page 16): Explain and why any offer by A would not be credible
Anderton and Carter illustrate pre-emptive war: Ea and Eb are the expected divisions of “income” if A strikes first or B strikes first, respectively. Note that both are inside the income possibility frontier, so that they reflect the waste of war. If A strikes first, B would prefer ex post any point on the possibility frontier between s and s’. However, since all of these points give less income to B than B attempting to strike first, then A knows any offer by B of such a division would not be credible. Only if Bb and Aa lines intersect in the interior of the possibility frontier will there be a possible negotiated solution that is credible, since both sides would prefer the negotiated division to what they could get by possibly striking first.
Pre-emptive war: What are the implications for this on conflict management. Three things again, a third party, reward, operations.
A third party can wage war and punish the side that strikes first, changing the costs of war thus making it a feasible space on the PPF. This would cause movement in the cost of war as above.
You can also reward peace by offering assistance and aid to the two sides that would shift the PPF outwards and make the contract space in the PPF.
Peace operations or inspectors would be a third-party to see if a first strike would occur and they would alert the other side that such an attack is happening. This would diminish the first strike advantage.
Pre-emptive war: What makes the outcome of war more likely
The bigger the advantage from the first strike the more likely war would occur as illustrated on the single line
If the cost of going to war is small or declines – the likelihood of war should go up as illustrated on the PPF
Preventive war: What is the context
Fearon’s second commitment problem leading to war is the case of preventive war. This case is essentially a multiperiod game, because the problem in preventive war is that there will be some future shift that benefits one player. Fearon has developed a model of rational preventive war where there is no disagreement about power. Fearon presents a subtle shift in the traditional argument from attacking now not for fear of attack in the future, but for fear of the settlement it would have to accept. Finally, there is no private information and no misunderstanding about motivations. The problem is one of an inability to commit to a policy in the future. In economics this problem is called “time inconsistency” and is equivalent to the need for sub-game perfection. A policy is said to be time inconsistent if there will be incentives to abandon the policy in the future because alternatives will become preferable. In other words, a promise by the rising state to not attack in the future would not be “sub-game perfect”. Therefore, a policy that may be the best for all concerned may not be feasible, even though it is desirable
Preventive war: Two states A and B bargain over some issue space that we can characterize as a simple linear division problem again. For simplicity we can just say that there is only one future period, period 2. The amount they are dividing in period 1 is V1 and in period 2 it is V2. Winning a war in period 1 means being able to take all of V1 in period 1 less the cost of war, plus all of the amount in period 2, V2. War in period 2 only means that there is a division agreed to in period one that adds up to V1, and then in period 2 the amount V2 less the cost of war goes to the victor. The losing side gets nothing the period it loses and any subsequent period.
What are the payoffs to the rising and declining powers as illustrated in an equation format?
If war occurs, Player A wins with probability p1 and player B wins with probability 1- p1. The cost of war will be C. So the expected outcome of having a war in period 1 for A is (p1) (V1 - C +V2), and for B it is (1-p1)(V1- C +V2). These two amounts clearly sum to less than V1 + V2 because of the cost of war, C, hence a Pareto superior ex ante agreement exists if the two sides can agree to divide the resources amongst themselves without war in such a way as to leave both at least as well off as if war occurred. If there is no change in the game, then a similar division could be found in period 2 to avoid war.
Preventive war: But what if the probability of victory in the second and subsequent rounds of the game increases in favour of A, the rising power? Then in period 2 player A should be able to get an even greater share of V2 by going to war. Specifically, A would expect in period 2 to get p2(V2 – C) from going to war, where p2 > p1. Similarly, B would expect to get (1-p2)(V2 – C). Side B knows that in period 2 it is relatively weaker and will get a smaller portion of V2; hence it might be tempted to attack A now and improve its chances of a better reward in period 2. A would like to make a division of V1 now that would reward B for not attacking now.
So B has to make a choice of accepting a peace deal with A and getting (at most) V1 + (1-p2)(V2-C). The “at most” part arises if A agrees to give B all of the available income in period 1 (V1) plus what b would expect to gain from war in period 2. If B chooses to fight in period 1, however, it can expect to get (1-p1)(V1- C + V2). So the question is, will B ever prefer fighting in period 1 to the peace deal?
B will prefer to attack A in period 1 if: these are the same conditions that can lower the risk of war
p2 gets very large relative to p1, so B’s decline in power is more dramatic; the intuition is that if B’s decline in power (reduction in the probability of winning) is large between the first and second periods, relative to the costs of fighting, then it will prefer to attack A now; i.e. a preventive war.
if the cost of war falls, making the losses from war smaller – if the cost of war increases in V2 then we can expect that war would be less likely because the rising power would have to pay more
if V1 is smaller, reducing A’s ability to bribe B into peace because they would know that if they attack now they can get V1 and V2
if V2 is bigger, making B more anxious to maximize its chances of winning all of V2 through war
Preventive war: Why is any arrangement deemed not credible by Fearon
Critically, what A wants to do is offer it all of the gains from period 1 and then in period 2 the contract space or more than the cost of war in period 2, for Fearon, there is no credible negotiable settlement. A would like to be able to offer B a better settlement in period 2 to prevent the war, but the most it can credibly offer now is all of V1; for A to offer B more out of V2 in period 2 would be known by B to be an “incredible” act, i.e. it is not sub-game perfect. Once period 2 was reached, A would have the incentive and capacity to renege on the agreement and force B to accept only (1-p2)(V2-C), the most it can expect from war
Preventive war general notes: Salami slicing, and comparison to pre-emptive war, and a note on time or multiple rounds.
The complexity can be increased if the probability of winning changes as a consequence of the division. Let’s say that after whatever division comes out of the initial agreement leaves A more powerful and hence raises its probability of winning a war from p1 to p2 (p2 > p1). This result would in turn leave it better off and thus more powerful and thus more capable of skewing the future division in its favour even further. This structure is related to “salami-slicing” policies.
In the pre-emptive case, both would like to see an advantage by attacking first. In the preventive case the advantage across the time periods grows so much for one player that the other cannot resist the urge to attack now (“first”) before the other has a potential advantage to do so. One game is simultaneous (pre-emptive) while the second game is sequential (preventive), but both effectively highlight the same bargaining problem
A note on time: if there are more periods it will be worse for player B because V2+V3+V4 is now a victor for player A the rising power – in the case that the probability of winning continues to go up for the rising power. But the probability matters, because some say China will ascend but eventually plateau then descend without the US having to go to war, so all US has to do is wait it out in that sense – so the probability of future periods really matters
Preventive war: What a conflict management institution can do, resources, cost of war, and support strategic balance
They could provide the resources necessary for A to bribe B in the first period
They could increase the cost of war in the first period if B decided to attack
Try to provide a military advantage or do things that will make B’s power less drastic and closer to A in the second period too – kind of odd like providing more weapons to the US because of China’s rise
Indivisibility as a cause of war: Typically, the “indivisible” good is portrayed as something territorial, such as an important location (e.g. the Temple Mount/Haram el-Sharif in Jerusalem), but it could also be ideological (e.g. “the state must be communist”), religious (e.g. “we must all be Protestants”).
Why is a lottery time-inconsistent in this case? Does it necessarily mean war will occur? Why or why not?
Only one party can have the indivisible desired good. War will allocate the good, but probabilistically and only with cost. An agreement to allocate it by lottery would be Pareto improving and Pareto optimal, but it would also be time inconsistent as the loser of the lottery would have the incentive to renege on a prior agreement.
The presence of indivisibility does not mean that war is a necessary outcome, however, as can be shown clearly in an Edgeworth box where there is a second good that can be used to compensate.
Indivisibility: Let Y be indivisible. The only possible divisions are on the red line AD, when player B gets (all of) Y and A gets none, but possibly some X; or on the green line CB where A gets (all of) Y and B gets none, but possibly some X.
For each graph, state whether there is a pareto efficient point, and whether war will occur?
1): Is there a better place they can be better off: Anywhere in between the two indifference curves
But they can’t share Y so you only have two options, either X gets all Y and in which case you’re down at the bottom doesn’t make them both better off, and there’s no point on the top line where they would both be better off. Thus indivisibly doesn’t mean war, but it does mean that there is no pareto efficient point to the status quo.
2): In this case any point on the top line where A get’s all of Y and B get’s some X would make both better off and is feasible – in this case there is a pareto superior solution
Indivisibility: Explain the last graph comparing each line for A and B and answering whether there is a settlement range, or whether war will occur.
If A expects to be on utility level UA1 after the costs of war in which it gets all of Y, then A will accept a settlement that gives at least XA1 even if Y goes to player B. If, alternatively, A anticipates the utility level associated with UA2 after fighting and getting Y, then the only settlement A would accept instead of war would be
In the case of UA2 and UB2, then war would be inevitable.
With UA1 and UB2 any division where B gets all of Y and A gets at least XA1 would be acceptable.
With UA2 and UB1 the contract space would have A getting all of Y and B getting at least XB1.
Finally, with UA1 and UB1 the possible settlements could be A getting all of Y and B getting at least XB1, or B getting all of y and A getting at least XA1.
Is indivisibility a reasonable argument for war:
There are economic solutions to this like dividing the good by time (5 years me then 5 years you) or by introducing a second good (I’ll give you a 100 billion – it really depends on how much I’m willing to give you)
There are outcomes where this would lead to war but not in every case