Weller's theorem (original) (raw)
Weller's theorem is a theorem in economics. It says that a heterogeneous resource ("cake") can be divided among n partners with different valuations in a way that is both Pareto-efficient (PE) and envy-free (EF). Thus, it is possible to divide a cake fairly without compromising on economic efficiency. Moreover, Weller's theorem says that there exists a price such that the allocation and the price are a competitive equilibrium (CE) with equal incomes (EI). Thus, it connects two research fields which were previously unrelated: fair cake-cutting and general equilibrium.
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| dbo:abstract | Weller's theorem is a theorem in economics. It says that a heterogeneous resource ("cake") can be divided among n partners with different valuations in a way that is both Pareto-efficient (PE) and envy-free (EF). Thus, it is possible to divide a cake fairly without compromising on economic efficiency. Moreover, Weller's theorem says that there exists a price such that the allocation and the price are a competitive equilibrium (CE) with equal incomes (EI). Thus, it connects two research fields which were previously unrelated: fair cake-cutting and general equilibrium. (en) Теоре́ма Ве́ллера — это теорема экономики. Она утверждает, что разнородный ресурс («торт») может быть разделён между n участниками с различными оценками значимости таким образом, что делёж будет как эффективным по Парето (англ. Pareto-efficient, PE), так и свободным от зависти (англ. envy-free, EF). Таким образом, можно разделить торт (разнородный ресурс) без нарушения экономической эффективности. Более того, теорема Веллера утверждает, что существует определённая цена, при которой распределение и цена находятся в (англ. competitive equilibrium, CE) с равным доходом (англ. equal incomes, EI). Таким образом, данная теорема связывает две области исследования, которые до этого были не связаны — это справедливое разрезание торта и общее равновесие. (ru) |
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| rdfs:comment | Weller's theorem is a theorem in economics. It says that a heterogeneous resource ("cake") can be divided among n partners with different valuations in a way that is both Pareto-efficient (PE) and envy-free (EF). Thus, it is possible to divide a cake fairly without compromising on economic efficiency. Moreover, Weller's theorem says that there exists a price such that the allocation and the price are a competitive equilibrium (CE) with equal incomes (EI). Thus, it connects two research fields which were previously unrelated: fair cake-cutting and general equilibrium. (en) Теоре́ма Ве́ллера — это теорема экономики. Она утверждает, что разнородный ресурс («торт») может быть разделён между n участниками с различными оценками значимости таким образом, что делёж будет как эффективным по Парето (англ. Pareto-efficient, PE), так и свободным от зависти (англ. envy-free, EF). Таким образом, можно разделить торт (разнородный ресурс) без нарушения экономической эффективности. (ru) |
| rdfs:label | Теорема Веллера (ru) Weller's theorem (en) |
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