Restatement (Second) of Contracts §71:

(1) To constitute consideration, a performance or a return promise must be bargained for.

(2) A performance or return promise is bargained for if it is sought by the promisor in exchange for his promise and is given by the promisee in exchange for that promise.

(3) The performance may consist of

(a) an act other than a promise, or

(b) a forbearance, or

(c) the creation, modification, or destruction of a legal relation.

(4) The performance or return promise may be given to the promisor or to some other person. It may be given by the promisee or by some other person.

Restatement (Second) of Contracts § 90. Promise Reasonably Inducing Action Or Forbearance:

(1) A promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person and which does induce such action or forbearance is binding if injustice can be avoided only by enforcement of the promise. The remedy granted for breach may be limited as justice requires.