The worst-case welfare loss from capping each agent at k items has an exact closed form, refining the asymptotic price of balancedness and extending to multiple item categories.
Optimal bounds on the price of fairness for indivisible goods
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The (Exact) Price of Cardinality for Indivisible Goods: A Parametric Perspective
The worst-case welfare loss from capping each agent at k items has an exact closed form, refining the asymptotic price of balancedness and extending to multiple item categories.