# Market clearing price for a single good with two consumers with different utilities

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.

• Please define "general theory with minimal assumptions". Cooperative game theory provides several different answers to this question, but I would not call the assumptions minimal. Oct 16 '21 at 5:35
• In the same vein as Giskard's comment, a non-cooperative game like take-it-or-leave-it game would give you one as well. We need more information. Oct 16 '21 at 6:38
• Well "minimal" is obviously relative. I meant the least amount of assumptions that will still allow for the determination of a single trade price. I finally found the relevant search terms and this section of Wikipedia mostly answers my question: en.wikipedia.org/wiki/Double_auction#Mechanism_design Oct 16 '21 at 13:43