In human groups and societies the basis and condition for their continued existence. It requires agreements, mutual tolerance, making and keeping promises and peaceful conditions.

1.   Here is a brief and somewhat formal explanation of social cooperation and agreement, where I presume the logic of propositional attitudes, and some logical facility in the reader, though I will explain the formula I use:

Conscious social cooperation involves the following, with

"aCFa" = "person a tries to cause the fact that a has property F"
"aDFa" = "person a desires the fact that a has property F"
"aKFa" = "person a knows the fact that a has property F"

First, there is a simple definition of cooperation, taken as involving two persons and their actions, and thus a four-place relation:

(1) CP(a,b,Fa,Gb) =def aCFa iff bCGb 
     Cooperation: a and b cooperate concerning Fa and Gb

which is to say that a tries to bring about Fa if and only if b tries to bring about Gb. Next, cooperation requires

(2) A(a,b,Fa,Gb) =def aDCP(a,b,p,q) & bDCP(a,b,Fa,Gb)
    Agreement: Both desire the cooperation mentioned in (1)

which is to say a and b cooperate only if both a and b desire to cooperate, and for this again they need to both know the agreement

(3) KAC(a,b,Fa,Gb) =def aKA(a,b,Fa,Gb) & bKA(a,b,Fa,Gb) -
     Knowledge of Agreement to Cooperate

which is to say that a and b both know that both desire to cooperate.

And now one can state when the successful social cooperation of a and b has taken place:

(4) KAC(a,b,Fa,Gb) & aCFa & bCGb & Fa & Gb -
     Successful social cooperation of a and b about Fa and Gb

Successful social cooperation of a and b about Fa and Gb amounts for a and b to have knowledge of their agreement to cooperate and for both to have done their agreed parts successfully, which will bring to a whatever good was produced by Gb and will bring to b whatever good was produced by Fa.

Next, it is relevant to note the following supposed truth about agreements, as a sort of minimal condition for their fairness, and as explanation for the mutual willingness to cooperate:

(5) A(a,b,Fa,Gb) --> v(a,aCFa) <= v(a,bCGb) &
                             v(b,bCGb) <= v(b,aCFa)

which is to say that in a minimal fair agreement to cooperate, the persons involved like to exchange because each likes what the other can offer more than what he can offer to the other in exchange.

Note that (5) can be derived from a presumption like this about both a and b, here only formulated for a, and using "v(a,q)" = "the value of q for a":

(6) aDC(a,b,Fa,Gb) --> v(a,aCFa) <= v(a,bCGb)

which is to say that a desires to cooperate only if a believes a will get at least as good as he gives.

It is noteworthy that none of the above requires money or a market in any sense, for all that need be involved are the value-assessments of the parties involved, that should make for the agreement stated by (5).

And it is also noteworthy that there are, between humans, very many ordinary social transactions that conform to the above, and that amount the exchanges of kindnesses, mutual help, barter, friendliness, politeness  etcetera, for most of the voluntary cooperation between humans conforms to the above, and needs nothing else, since if the conditions are met, both parties involved by their own values profit from the transaction (or at least don't loose by it).

However, it is true that the above may lead to situations that, at least after the fact of exchange, may be considered quite unfair - for example, as the Indians may have soon found after bartering away Manhattan for a handful of trinkets to the Dutch that they were deceived, and could have received much more than they got out of this nation of sly and dishonest traders.

One can take care of this difficulty in various ways, and I will here do it as follows:

(7) v($,Fa) sim v($,Gb) =d (xe$)xK(pr((Eye$)A(x,y,Fx,Gy))>1/2)

which is to say that I suppose acts and commodities in a society $ have a social value that is similar if and only if everybody in the society knows that they probably can find someone in the society to make a fair exchange with the goods or acts involved.

And now one can define

(8) FA(a,b,Fa,Gb) = d A(a,b,Fa,Gb) &
                             aK(v($,Fa) sim v($,Gb)) &
                             bK(v($,Fa) sim v($,Gb))

which is to say that a fair agreement amounts to getting a fair deal for a fair price, where the deal is fair because both parties agree they are willing to exchange, and the price is fair because both parties know they could get a similar deal elsewhere in the society, if they tried.

Note though that it is still not necessary to use money, and that again there are many transactions between humans in a society that are fair agreements as defined, whether or not they involve money.