Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence of Models of Cake-Cutting Protocols   The cake-cutting problem involves dividing a heterogeneous, divisible
resource fairly between $n$ agents. Br\^{a}nzei et al. [6] introduced {\em
generalised cut and choose} (GCC) protocols, a formal model for representing
cake-cutting protocols as trees with "cut" and "choose" nodes corresponding to
the agents' actions, and if-else statements.
  In this paper, we identify an alternative and simpler extensive-form game
model for cake-cutting protocols, that we call {\em branch choice} (BC)
protocols. We show that the class of protocols we can represent using this
model is invariant under certain modifications to its definition. We further
prove that any such protocol can be converted to a restricted form in which the
agents first cut the cake and then get to choose between various branches
leading to different allocations. Finally, we show that this model has the same
expressive power as GCC protocols, i.e. they represent the same class of
protocols up to a notion of equivalence involving the bounds on envy that each
agent can guarantee for themselves. For this purpose, we introduce a new notion
of envy-equivalence of protocols.

25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga