Cutting a cake for infinitely many guests
Zsuzsanna Jank\'o, Attila Jo\'o

TL;DR
This paper introduces new, simpler algorithms for fair division with irrational entitlements and proves that fair division is always possible even with infinitely many players, extending classical methods.
Contribution
The paper presents novel algorithms based on the Last diminisher technique for fair division with irrational entitlements and establishes the existence of fair division among infinitely many players.
Findings
New algorithms for irrational entitlements
Existence of fair division with infinitely many players
Simpler methods than previous approaches
Abstract
Fair division with unequal shares is an intensively studied recourse allocation problem. For , let be an atomless probability measure on the measurable space and let be positive numbers (entitlements) with . A fair division is a partition of into sets with for every . We introduce new algorithms to solve the fair division problem with irrational entitlements. They are based on the classical Last diminisher technique and we believe that they are simpler than the known methods. Then we show that a fair division always exists even for infinitely many players.
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Taxonomy
TopicsGame Theory and Voting Systems · Economic theories and models · Auction Theory and Applications
