Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coalitional Permutation Manipulations in the Gale-Shapley Algorithm   In this paper, we consider permutation manipulations by any subset of women
in the men-proposing version of the Gale-Shapley algorithm. This paper is
motivated by the college admissions process in China. Our results also answer
an open problem on what can be achieved by permutation manipulations. We
present an efficient algorithm to find a strategy profile such that the induced
matching is stable and Pareto-optimal (in the set of all achievable stable
matchings) while the strategy profile itself is inconspicuous. Surprisingly, we
show that such a strategy profile actually forms a Nash equilibrium of the
manipulation game. In the end, we show that it is NP-complete to find a
manipulation that is strictly better for all members of the coalition. This
result demonstrates a sharp contrast between weakly better off outcomes and
strictly better-off outcomes.

5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int