PPAD-Completeness of Contiguous Envy-Free Cake Cutting with Additive Valuations
We prove that computing a complete contiguous $\varepsilon$-envy-free cake allocation is PPAD-complete for normalized rational piecewise-constant additive valuations. The hardness holds even when $\varepsilon$ is given in unary, and even when every density takes only two values, which are the same for all agents, and is piecewise constant with at most six breakpoints. As a consequence, computing an exact contiguous envy-free allocation is also PPAD-complete, and the hardness holds under the same restrictions on the densities. Our key ingredient is to assign prices to the pieces so that, in every approximately envy-free allocation, all prices are nearly equal, regardless of how the pieces ...
| Authors | Yasushi Kawase, Bodhayan Roy, Mohammad Azharuddin Sanpui |
|---|---|
| Primary category | cs.GT |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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