Consider a single multi-dimensional path-based agent who wishes to purchase at most one of two items....

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Consider a single multi-dimensional path-based agent who wishes to purchase at most one of two items. The agent's quantile q is drawn U[0,1] and her type given by 11(q) = 2-g and t2(q) = 4 - 4q. In other words, her value for item 1 is U[1,2] and her value for item 2 is U[0,4]. As described in the textbook, the agent's utility for allocation x E [0,1P with E; x;s 1 and paymentp is E; t;(q) Xj - p; allocation x; is interpreted as specifying the probability that the agent receives item j; the constraint E; X;s 1 reflects the unit-demand constraint of the agent. Identify the revenue optimal mechanism and prove that it is correct. Consider a single multi-dimensional path-based agent who wishes to purchase at most one of two items. The agent's quantile q is drawn U[0,1] and her type given by 11(q) = 2-g and t2(q) = 4 - 4q. In other words, her value for item 1 is U[1,2] and her value for item 2 is U[0,4]. As described in the textbook, the agent's utility for allocation x E [0,1P with E; x;s 1 and paymentp is E; t;(q) Xj - p; allocation x; is interpreted as specifying the probability that the agent receives item j; the constraint E; X;s 1 reflects the unit-demand constraint of the agent. Identify the revenue optimal mechanism and prove that it is correct.

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We contrast the projected efficiency of revenuemaximizing mechanisms with that of efficiencymaximizi... View the full answer