Identifying a valid offer
An offer is an expression of willingness to contract on specific terms, made with the intention that it is to become binding as soon as it is accepted by the person to whom it is addressed. A binding contract is concluded once an offer has been accepted unconditionally.
In general, we have to identify a valid offer and a valid acceptance of that offer to identify an agreement. Then, what is a valid offer?
It must be communicated, so that the offeree may accept or reject it.
It may be communicated in writing, orally or by conduct.
It may be made to a particular person, to a group of persons, or to the whole world (Carlill v Carbolic Smoke Ball Co.)  .
It must be definite in substance.
It must be distinguished from an invitation to treat.
We can classify “offers" into two categories, namely, unilateral offer and bilateral offer. The distinction between unilateral and bilateral arrangements is important with regard to advertisements, communication of acceptance and revocation of offers.
A bilateral offer is a two-sided offer in which both parties are committed to the transaction and have a contractual obligation to perform in accordance with their respective promises. They are usually considered invitations to treat on the grounds that they may lead to further bargaining. It is more common and general rules on contract usually apply on them. These general rules related here are, to name but a few, advertisements of a bilateral nature are generally invitation to treat only, acceptance must be communicated to the offeror.
Acceptance for bilateral contract cannot be offer. It can be illustrated by Partridge v Crittenden  . In this case, a person who placed an advertisement for sale of Bramblefinch was charged with unlawfully offering for sale a wild bird which was against the Protection of Birds 1954. However, the conviction was quashed on the grounds that the advertisement was not an offer but an invitation to treat. It is argued that if an advertisement is an offer, then the trader will have to supply the quantity ordered when the stock available to do so is limited. Similarly, in Grainger & Son v Gough  , Lord Herschell said that the transmission of a price-list does not amount to an offer to supply an unlimited quantity of the wine described at the price named, since if it were an offer the so-called “offeror" might find himself involved in any number of contractual obligations which he would be quite unable to carry out, for his stock of wine being necessarily limited.
A unilateral offer is a one-sided offer whereby the offeror makes a promise in return for the performance of a stipulated act, without the offeree’s having made any counter-promise to perform the required act or forbearance. The offer is accepted by the performance of the requested action. Since the acceptance is the performance of the stipulated act and performing this act may be a continuous act, the general principle is that the offer may be revoked at any time before the act is completely performed. However, it may not be possible to revoke a unilateral offer once the offeree has started to perform. (Errington v Errington  )
To illustrate unilateral offers, the landmark case Carlill v Carbolic Smoke Ball is always valuable. In this case, Mrs. Carlill accepted the unilateral offer by using the carbolic ball and therefore a binding contract is concluded. In this case, several characteristics of a unilateral offer were stated. For example, the offeror may waive the normal requirement of communication of acceptance, wither expressly or impliedly. Also, Lord A.L. Smith LJ stated that there was no express requirement that acceptance be notified. Moreover, Lord Lindley LJ and Lord A.L. Smith LJ considered that the promise by the company is supported by consideration in the sense of a benefit to the offeror company and/or a detriment to the offeree.
From this case, there are several points about unilateral offers can be concluded. Firstly, although generally an advertisement is an invitation to treat, if the advertisement requests the performance of an act (which constitutes good consideration for the promise by itself) then the advertisement will be an offer. Secondly, in a unilateral offer, acceptance is made by fully performing the required act and it needs not be communicated to the offeror in advance unless there has been an express indication that notification is required. Thirdly, as it is impractical to communicate the revocation of an offer to the whole world since it is not possible to identify the potential offerees, it is considered sufficient if the revocation is communicated by a notice “having the same notoriety" (using the same channel used to communicate the original offer). (Shuey v US) 
Therefore, we can differentiate unilateral and bilateral offers in advertisements, communication of acceptance and revocation of offers. While an advertisement of a unilateral nature is more likely to be an offer that of a bilateral nature is generally invitation to treat only. Also, prior notice from the offeree to accept the offer is not required as no one is legally obliged to perform, or even attempt the act. Moreover, unilateral offers may be made to the whole world, and we may have to consider whether a revocation can take place as the offeree may have started to perform the acceptance.
All in all, I believe unilateral offer should be regarded as a valid offer. Although it may not always fit in general cases of contracts, its being exceptional does not rule out its ability to fulfill the aforementioned five conditions to make it a valid offer. In fact, it is more likely to be a valid offer than bilateral offer does.
According to Currie v Misa  , a valuable consideration in the eyes of the law may consist of either some right, interest, profit or benefit to one party; or some forbearance, detriment, loss or responsibility given, suffered or undertaken by the other.
Consideration must move from the “promisee". It generally means that the party wishing to enforce the other party’s promise must prove that he has personally provided something of value in return. In Tweddle v Atkinson  , the plaintiff cannot sue the estate of Guy because he himself did not provide consideration to enforce Guy’s promise to pay him the money for marrying Guy’s daughter. The one who provided consideration is in fact the plaintiff’s father.
Consideration needs to be sufficient but need not be adequate. As it is for the parties themselves to make their own bargain, the consideration need only have “some value in the eyes of the law". The value of the consideration may be slight as £1 was held to be good consideration for an option to buy a house in Mountford v Scott  .
Traditionally, performance of an existing duty like a duty imposed by law or an existing duty owed to the other party have no value in the eyes of law. The promise, in such situations, has suffered no legal detriment since he has done only what he was already obliged to do; the promisor gets no legal benefit from the performance to which he was already entitled. Therefore, this could not provide sufficient consideration in return for the promise of additional reward. However, does it mean it will never amount to consideration?
Performance of a duty imposed by law (Public duty)
Performance of a duty imposed by law is generally not a good consideration. In Collins v Godefroy  , Lord Tenerden CJ held that a promise to pay a fee to witness who has been properly subpoenaed to appear in court was made without consideration as the witness had a public duty to attend.
However, if a promise has done more than he was legally obliged to do, that will constitute consideration for a promise to pay. This can be well illustrated in Ward v Byham  . In this case, the father of an illegitimate child promised to pay the child’s mother up to £1 a week allowance for her provided that she can prove that the child will be well looked after and happy. Lord Denning LJ held that the promise was supported by consideration and therefore enforceable. The majority considered that although the mother was required by statute to maintain her child, she had gone beyond her statutory duty by complying with the father’s quest. Therefore, Lord Denning LJ considered that the factual benefit to the father was sufficient for his promise to be supported by consideration.
Performance of a contractual duty owed to the promisor
This arises in the context of a promise to alter an existing contract between parties. In Stilk v Myrick  , two sailors deserted a ship during a voyage and the captain was unable to find replacements. The remaining crew members were promised extra wages for sailing the ship back to London but the captain refused to pay on arrival. The court held that the crews were already bound by their contract to meet the normal emergencies of the voyage and that there was no consideration as the sailors had already contracted to work the ship home.
However, the case is different in Hartley v Ponsonby  . In this case, nearly half the crew deserted. The Queen’s Bench held that the crew was so reduced that it was dangerous to life to sail and unreasonable for the master to require his crew to do so. This discharged the contracts of the remaining sailors and so the sailors were free to make a new bargain as they were in the same position as any other free seamen, so the captain’s promise to pay additional wage was enforceable. Also, in Williams v Roffery  Bros, the court held that if a party to an existing contract later agrees to pay an ‘extra bonus’ in order that the other party performs his obligations under the original contract, then the new agreement is binding if the party agreeing to pay the bonus has obtained new practical or factual advantage or avoided a disadvantage.
Performance of an existing contractual duty to a third party
The courts have long recognized that mere performance of an existing duty owed to a third party can be good consideration for the promisor’s promise of “reward". One case that illustrates this is Scotson v Pegg  . In this case, Scotson contracted to supply a cargo of coal to a third party, X, or to anyone X nominated. Scotson sued Pegg, a third party, claiming that their promise to deliver coal to him was consideration for his promise to unload it. Peg claimed that this could not be consideration since Scotson as already bound to supply the coal under contract with X. The court upheld Scotsons’ claim because their agreement with the defendant may be a detriment to them, and in that it prevented them from choosing to break their contract with X.
Part payment of a debt
The basic rule here is that payment of a smaller sum will not discharge the duty to pay a higher sum. In Pinnel’s Case  , the Court held that in such circumstances the debtor must provide consideration for the creditor’s promise to release him as part payment constitutes no good consideration. Traditionally, the factual benefit that might accrue to the creditor from securing some payment rather than nothing at all was not regarded as sufficient and some separate consideration was required. As in Foakes v Beer  , the House of Lords held that on its true construction, their agreement merely gave Foakes time to pay or was intended to cover interest as well. However, if the payment is settled in a different form, for instance, part payment plus some other form of consideration, or payment before the due date, sufficient consideration may then be constituted.
Based on the above analysis, I believe that, even though some cases may be controversial, I do NOT agree that performance of an existing duty will never amount to consideration.