[hsqpxydj] Price formation for prostitution

A prostitute and potential client negotiate a contract prior to sex.  This may be an economic situation more complicated than, and different from, the price formation of any other good.

The client has negative utility of paying money and imperfect information about the (hopefully positive) utility of having sex.  Similarly, the prostitute has positive utility of gaining money and also imperfect information about the utility of having sex.  Of course, a deal should only be reached if both participants' net utilities are positive.

The interesting feature of this negotiation is both participants' imperfect information of the utility of having sex.  These utilities are highly dependent on the "chemistry" between the participants and is assumed to have high variance and be very difficult to estimate for both participants.  The variance (or its square root) is assumed to dwarf the utility of money for both participants. 

The dependence on "chemistry" is assumed to thwart screening and signaling mechanisms traditionally available for imperfect information games.  For example, a credible review of this prostitute by a previous client is assumed entirely useless to this client; the chemistry may be totally different.

Are these assumptions artificially too extreme? (Probably.)

How can price formation work in the presence of this kind of uncertainty, especially in both participants?  Can an expected mutually beneficial deal be reliably reached?

Furthermore, every prostitute is different and every client is different, so there is the monopoly effect of product differentiation going on in both directions.

Is there any other good that has similar characteristics?  Is prostitution so qualitatively different from everything else such that we cannot reason about it with analogies to other products?  This becomes relevant if prostitution is legalized, but we need to regulate it to correct market failures.  Will we even be able to detect if market failure is occurring?

Compare this situation to a producer selling a simple object. The utility of giving up the object does not depend heavily on to whom the producer sells it. Similarly, the consumer's utility of getting the good does not depend heavily on from whom the consumer buys it.

If a price of zero is mutually beneficial, i.e., they both get positive utility from sex, then this becomes relevant to dating.