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Conditions one might impose on fair allocation procedures are introduced. Nondiscrimination requires that agents share an item in proportion to their entitlements if they receive nothing else. One-agent monotonicity requires that such a change should not hurt the first agent, limited monotonicity that the solution should not change. For prices, the former implies convexity in the smaller of the two valuations, the latter linearity. In either case, the price is at least their average and hence spiteful.
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