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Envy-free theory addresses the dilemma of allocating scarce resources through the use of complex mathematical formulae so that each individual believes that his or her share is equal to or better than that of anyone else who takes part in this resource sharing. The purpose of devising these mathematical formulae is to reduce or eliminate the envy that one individual may feel against another after the resource in question is allocated.

Over the past 50 years, mathematicians have developed several theories on how to fairly distribute scarce resources and have used the cutting of a cake to represent these devised formulae. Curiously, the application of envy-free theory dates back to more than 2,800 years ago. In his literary work Theogeny, Hesiod cited an example in which ...

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