Method and apparatus for selecting a desirable allocation of bids in a combinatorial exchange setting
First Claim
1. A method of selecting a desirable allocation of bids in a combinatorial exchange setting comprising:
- (a) providing a plurality of bids, each of which includes at least one item, a quantity for each item and price for all of the item(s) and their quantities;
(b) selecting an adversarial allocation of the bids;
(c) determining as a function of the adversarial allocation of the bids (1) a candidate allocation of the bids and (2) a value of a minimax regret related to a utility associated with the adversarial allocation minus a utility associated with the candidate allocation;
(d) determining as a function of the candidate allocation (1) a new adversarial allocation of the bids and (2) a value of a maximum regret related to a utility associated with the new adversarial allocation minus a utility associated with the candidate allocation;
(e) if the current value of the maximum regret is greater than the current value of the minimax regret, determining as a function of the adversarial allocation(s) (1) a new candidate allocation of the bids and (2) a new value of minimax regret related to a utility associated with the adversarial allocations minus a utility associated with the new candidate allocation;
(f) determining as a function of the new candidate allocation (1) a new adversarial allocation of the bids and (2) a new value of maximum regret related to a utility associated with the new adversarial allocation minus a utility associated with the candidate allocations; and
(g) repeating steps (e) and (f) until the current value of maximum regret is not greater than the current value of minimax regret.
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Abstract
A desirable allocation of bids in a combinatorial exchange can be selected by determining a first candidate allocation of the bids and a first value of a minimax regret, related to the difference in utility between the adversarial allocation and the candidate allocation, as a function of a first adversarial allocation of the bids. Based on the first candidate allocation, a second adversarial allocation of the bids and a first value of a maximum regret related to the difference in utility between the new adversarial allocation and the utility of the candidate allocation can be determined. When the value of the maximum regret is greater than the value of the minimax regret, the candidate allocation can be designated as the desirable allocation.
6 Citations
14 Claims
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1. A method of selecting a desirable allocation of bids in a combinatorial exchange setting comprising:
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(a) providing a plurality of bids, each of which includes at least one item, a quantity for each item and price for all of the item(s) and their quantities; (b) selecting an adversarial allocation of the bids; (c) determining as a function of the adversarial allocation of the bids (1) a candidate allocation of the bids and (2) a value of a minimax regret related to a utility associated with the adversarial allocation minus a utility associated with the candidate allocation; (d) determining as a function of the candidate allocation (1) a new adversarial allocation of the bids and (2) a value of a maximum regret related to a utility associated with the new adversarial allocation minus a utility associated with the candidate allocation; (e) if the current value of the maximum regret is greater than the current value of the minimax regret, determining as a function of the adversarial allocation(s) (1) a new candidate allocation of the bids and (2) a new value of minimax regret related to a utility associated with the adversarial allocations minus a utility associated with the new candidate allocation; (f) determining as a function of the new candidate allocation (1) a new adversarial allocation of the bids and (2) a new value of maximum regret related to a utility associated with the new adversarial allocation minus a utility associated with the candidate allocations; and (g) repeating steps (e) and (f) until the current value of maximum regret is not greater than the current value of minimax regret. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. An apparatus for selecting a desirable allocation of bids in a combinatorial exchange comprising:
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means for receiving a plurality of bids, each of which includes at least one item, a quantity for each item and price for all of the item(s) and their quantities; means for forming a first adversarial allocation of the bids; means for determining as a function of the first adversarial allocation of the bids (1) a first candidate allocation of the bids and (2) a first value of a minimax regret related to a difference between a utility associated with the adversarial allocation and a utility associated with the candidate allocation; means for determining as a function of the first candidate allocation (1) a second adversarial allocation of the bids and (2) a first value of a maximum regret related to a difference between a utility associated with the new adversarial allocation and a utility associated with the candidate allocation; and means for producing a visual display of the first candidate allocation as the desirable allocation when the first value of the maximum regret is not greater than the first value of the minimax regret. - View Dependent Claims (10, 11, 12, 13, 14)
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Specification