Consider a bilateral trading problem in which two agents initially own one unit of the homogeneous good. Each agenti = 1,2's valuation per unit consumed of the good is v₁, which is independently drawn from a uniform distribution on [0,1].
(a) Characterize the ex post efficient allocation rule.
For the remaining problems, consider the following mechanism: Each agent i submits bid b₁; if b₁ > by, agent 1 buys agent 2's endowment and instead pays him by; if by > b₁, agent 2 buys agent 1's endowment and pays her b₁.
(b) Derive a symmetric linear equilibrium of the induced game by this mechanism, in which each agent makes a bid of
bi (vi) a + Boj. =
(c) Illustrate whether the allocation rule in part (a) is Bayesian implementable via the given mechanism.