It is well-known that optimal (i.e., revenue-maximizing) selling mechanisms in multidimensional type spaces may involve randomization. We study mechanisms for selling two identical, indivisible objects to a single buyer. We analyze two settings: (i) decreasing marginal values (DMV) and (ii) increasing marginal values (IMV). Thus, the two marginal values of the buyer  are not independent. We obtain sufficient conditions on the distribution of buyer values for the existence of an optimal mechanism that is deterministic. In the DMV model, we show that under a well-known condition , it is optimal to sell the first unit deterministically . Under the same sufficient condition, a bundling mechanism (which is deterministic) is optimal in the IMV model. Under a stronger sufficient condition  , a deterministic mechanism is optimal in the DMV model. Our results apply to heterogenous objects when there is a specified sequence in which the two objects must be sold.
It is well-known that optimal (i.e., revenue-maximizing) selling mechanisms in multidimensional type spaces may involve randomization. We obtain conditions under which deterministic mechanisms are optimal for selling two identical, indivisible objects to a single buyer. We analyze two settings: (i) decreasing marginal values (DMV) and (ii) increasing marginal values (IMV). Thus, the values of the buyer for the two units are not independent. We show that under a well-known condition on distributions~(due to McAfee and McMillan (1988)), (a) it is optimal to sell the first unit deterministically in the DMV model and (b) it is optimal to bundle (which is a deterministic mechanism) in the IMV model. Under a stronger sufficient condition on distributions , a deterministic mechanism is optimal in the DMV model. Our results apply to heterogeneous objects when there is a specified sequence in which the two objects must be sold.
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study mechanisms
obtain conditions under which deterministic mechanisms are optimal
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two marginal
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for the two units
D
obtain sufficient conditions on the distribution of buyer values for the existence of an optimal mechanism that is deterministic. In the DMV model, we
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,
on distributions~(due to McAfee and McMillan (1988)), (a)
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. Under the same sufficient condition, a bundling mechanism (which is deterministic) is optimal
in the DMV model and (b) it is optimal to bundle (which is a deterministic mechanism)
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on distributions
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heterogenous
heterogeneous