Say I have a single indivisible good that is randomly allocated to one of two consumers. The first consumer's utility for the good is \$5 and the second consumer's utility for it is $10.
If the good is allocated to the 2nd consumer, we have a Pareto equilibrium and no trades should occur.
But if the good is allocated to the first consumer, both consumers will benefit from trading the good at any price between \$5 and $10.
My question is whether there is any general theory with minimal assumptions that will give a single price at which the trade will occur? Assume that either both consumers have perfect or no information about each other's utilities.