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.

  • $\begingroup$ 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. $\endgroup$
    – Giskard
    Oct 16 '21 at 5:35
  • $\begingroup$ 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. $\endgroup$ Oct 16 '21 at 6:38
  • $\begingroup$ 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 $\endgroup$
    – robsmith11
    Oct 16 '21 at 13:43

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