Hypotheses

As always, only the performance of a task can increase the total utility (by Vb(q) −

Cs(q)), non-performance leads only to the payment of decommitment fee (which

does not increase welfare in the society, it merely moves it from one party to another) and possibly also the seller’s costs (Ec = D(t)Cs(q)). The latter is

a waste for the society, because it produces no benefit. So, the problem is to maximise the performances and to minimise the decommitments. Of course these two goals are contradictory: the decommitments would be minimised by having no contracts (no risk of decommitments), but the maximisation of performances might lead to a large number of contracts. With no contracts, the total utility in the market is zero. Taking some contracts, the utility might be positive and taking too many contracts, the total utility may even be negative (the costs of decommitments outweighing the benefits from the performances).

The basic idea is then to find a balance between the two and instead of getting just some contracts, getting contracts that are more likely to be performed. In our setting, where the buyers and sellers are homogeneous in terms of their reliability, the only way to improve the chances of success is to wait longer before entering into a contract. However, as explained, there are risks involved in waiting: if agents wait too long, they might not get contracts at all. Therefore the risk of decommitment has to be considered with a chance of getting a contract in the first place. When the risk of later decommitment is small, it may be more important to secure a contract whenever an opportunity arises. But when a decommitment is very likely, waiting is often more prudent.

As explained, the parties can use the contract price very effectively as a means of ensuring positive expected utility for themselves no matter what the decommit- ment policy is (within reason5_{) and if both parties are doing that then the expected}

utility for the society is always non-negative (positive if there are any contracts) in any setting in the long run. Sometimes it is even possible that one party alone, by taking the contract decision into account, can ensure positive expected utility. This requires that the only source of negative total utility, the seller’s possible costs, is clearly in one party’s responsibility and that party takes the contract decision into account. Other cases will not adapt correctly and will perform badly when the effect probability is high, because they will enter into contracts that are never going to be performed causing costs to the sellers. Thus, we contend:

Hypothesis 9. When only one of the parties can be affected and the decommitment fee is either compensatory or Constant 0.0, the case where both parties take contract decision into account is no worse than any other policy and it will be better than the case where neither

5_{For example, Not Allowed or policies with very high decommitment fees, strict limits on} the price or similar factors, can make this adjustation impossible and mean that society suffers (i.e. no mutually agreeable contracts can be found, although with less strict commitments such contract could be found).

party considers the contract decision or the case where only one party does so, if the party in question is not liable for the provider’s possible costs according to the decommitment policy. The difference is clearest with high effect probabilities.

As also explained earlier, serious over-compensation (like Constant 1.0 ) will make the decommitment on one hand, a potentially disastrous situation for the potential decommitter and, on the other hand, very attractive for his opponent. This means that the affected party that takes the contract decision into account will need to be very careful. Specifically, it will want to enter a contract only close to the deadline (the risk of decommitment is smaller) and/or have a very high utility (high reservation price for the sellers and low reservation price for the buyers) in the case it is able to perform to balance things out. In contrast, his opponent may well be interested in accepting very bad contracts (from its point of view), if that gives him a chance of getting the high decommitment fee if the opponent fails. On their own these two tendencies influence the decisions into opposite directions: when the affected party alone takes the contract decision into account, it will want to wait for longer and longer and this leads to less and less contracts when the effect probabilities increase until with very high effect probabilities there is (almost) no contracts. The very high fee makes this effect stronger and makes the potentially affected party go to great lengths to avoid too big a risk of that fee. So when the fee over-compensates the victim’s loss as badly as the Constant 1.0 policy does, the potentially affected party overdoes this (is too careful to avoid contracts) and this will affect adversely the total utility when it alone will consider the contract decision. The total utility is going to be worse than in the case where neither party takes the contract decision into account in intermediate effect probabilities. In very low probabilities there are not enough decommitments to make a significant difference and since staying out of risky contracts will ensure non-negative expected total utility it will be able to outperfom the case where neither will take the contract decision into account when the effect probabilities are very high and the expected total utility becomes negative.

On the other hand, when only the decommitter’s opponent takes the contract decision into account, the effect is opposite: the opponent will want a contract as soon as possible. This is because it prefers the non-performance and is willing even to take a worse contract to secure a chance to get the high fee. The earlier it manages to lure the potential decommitter into a contract, the more likely the decommitment will occur. From the total utility’s point of view, this is of course counter-productive and, therefore, in the case where only the victim takes the

contract decision into account, the results are likely to be even worse than when no party takes the contract decision into account. This will happen especially with high effect probabilities when the fee is very likely.

In case the potential decommitter is the seller, there is also its own costs to con- sider. In case of decommitment, the seller will have to pay not only an overcom- pensatory fee but also its own possible costs. This makes the seller even more reluctant to enter into contracts and the effects described above are likely to be even stronger. Specifically, we contend:

Hypothesis 10. When only one of the parties can be affected and the decommitment policy is Constant 1.0, both cases where only one of the parties takes the contract decision into account will perform worse than the case where neither takes the contract decision into account at least with some effect probabilities. For the case where the decommitter considers the contract decision, this occurs with low to intermediate effect probabilities and for the case where the victim considers it, especially with high probabilities. When the seller is the decommitter, these effects are stronger.

When only one of the parties is affected, the decision-making of a participant involves either the possibility that they themselves will have to decommit or that their opponent might have to decommit at some point. When both parties can be affected, both of these factors need to be considered at the same time. We only consider cases where the effect probability is the same for both parties. This means that the probabilities for the player itself or its opponent having to decommit is the same and in both Constant policy cases, also the decommitment fee is the same so these things cancel each other out in the case of the buyer and it is not therefore too worried about possible decommitments. However, for the seller the situation is significantly different because in addition to the fees, it has to consider the possibility that it will have to cover its own costs. This can occur both when it has to decommit itself and when the other party decommits (fees it pays or receives cancel each other out). This will mean that the seller will do all the necessary adjustments and the buyer none.

The compensatory cases are more interesting because the parties’ profits and costs are different. Therefore the fees do not cancel each other out, instead they have to be considered. This means the parties will have to consider their profits and the costs they would receive as compensation if the other party decommits and their

Case Ub Us Ub+s

Buyer Decommits −f = −Ecs f − Ecs = 0 −Ecs

Seller Decommits f = 0 f − Ecs = −Ecs −Ecs

Table 6.1: _{Utilities in the Reliance Damages policy.}

opponent’s profits and costs that would have to be compensated for if they are forced to decommit. In the Reliance Damages policy case, either party considering the contract decision alone will not be able to cover all cases. This is because both parties alone consider only one of two cases. The buyer considers the utilities in the Ub column and the seller the utilities in the Us column in table 6.1. Both of

them ignore the seller’s costs in one of the two cases, because either the buyer compensates them or ignores them. Only when both parties consider the contract decision at the same time will the seller’s costs be considered by one party in all cases and therefore, the case where both consider the contract decision is likely to outperform other cases with intermediate effect probabilities (when there are enough decommitments, but there are still enough contracts).

The Expectation Damages case is a bit different. The expected utilities for each case are as shown in table6.2. Now, under this policy, the buyer will get its full util- ity with the probability of P (success)+P (seller decommits)+1

2P (both may decommit)

and it will have to pay the seller’s profits and costs with the probability of P (buyer decommits) + 1

2P (both may decommit). If the buyer’s utility in case of

success is high enough, compared to the compensation the buyer has to pay in case of its own decommitment, the buyer is willing to negotiate and enter a contract even when performance is very unlikely. In the extreme case, let P (buyer effect) = P (seller effect) = 1. This means that P (both may decommit) = 1 and all other probabilities are zero. Now, the buyer’s expected utility is:

Ub =

1

2(Vb(q) − p) + 1

2(−p + C(q) − Ecs).

This will be positive, if Vb(q) − p > −p + C(q) − Ecs, so even if the decommitment

is a certainty, the buyer is willing to enter a contract if the utility in case the seller decommits first (= U (success)) is greater than the fee it has to pay in case it has to decommit first. In other words, if the buyer is able to get a good contract (low price), it will be willing to take it even if it will know that it will never be performed. A similar logic applies to the buyer and the logic can also be extended to less extreme cases. Therefore when either party alone considers the contract decision, it can enter into contracts even if performance is very unlikely or even

Case Ub Us Ub+s

Buyer Decommits −f = −p + C(q) − Ecs f − Ecs = p − C(q) −Ecs

Seller Decommits f = Vb(q) − p f − Ecs= p − Vb(q) − Ecs −Ecs

Table 6.2: _{Utilities in the Expectation Damages policy.}

impossible, as long as the utility in case of success is large enough compared to the fee it has to pay in case of failure. When the other party does not consider the contract decision, it will be willing to enter into such contracts. But when both parties take the contract decision into account, no contract can be acceptable to both of them when P (both may decommit) = 1 (for any given contract, both parties cannot have higher utility in case of success than in case of failure at the same time). Also in less extreme situations, the parties will be more careful. We therefore contend:

Hypothesis 11. When both can be affected and decommitment policy is compensatory (either Reliance or Expectation Damages), the case where both parties consider the contract decision will always be at least as good as any other setting and it will be better at least some of the time.

The price can be effectively used between the parties to distribute the risks in an effective way. In this distribution, it makes little difference what the decommit- ment policy is, but all policies should perform roughly the same. However, given that the price is limited to the interval [0, 1] it may well be that the parties are unable to adapt properly in case the fee is heavily overcompensatory and only one of the parties can be affected. This is because the party not affected is unable to set the price so that the party affected would be able to find that acceptable and not all parties will be able to wait until the risk would be acceptable (because of their deadlines and effects). The problem is less pronounced when both parties can be affected because the risk of an oversized decommitment fee is more evenly distributed. Thus:

Hypothesis 12. When only one of the parties can be affected, the Constant 1.0 policy will perform worse than the other policies.

The performance of different policies depends of course on the information they have. We have assumed that both the buyer and the seller will know when the

seller pays its cost and therefore can calculate the expected cost of the seller accurately. However, already a small change like not knowing the time accurately will affect the buyer’s ability to estimate his risks in the compensatory policies. So, if instead of Ec = tdelivery−tcost

tdelivery−tcontractCs(q), all times after the contract is formed

are equally likely and, then Ec = 1₂Cs(q). This sometimes overestimates and

sometimes underestimates the seller’s expected cost and will mean that the buyer sets his reservation price on a slightly wrong level. This small error alone is enough to decrease the total utility in cases where the buyer is affected and the buyer takes the contract decision into account. We therefore contend:

Hypothesis 13. When the buyer is affected, but does not know the time the seller has to pay its cost, the performance in terms of total utility suffers in compensatory policies.