Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual Selection Games   Often, a given selection game studied in the literature has a known dual
game. In dual games, a winning strategy for a player in either game may be used
to create a winning strategy for the opponent in the dual. For example, the
Rothberger selection game involving open covers is dual to the point-open game.
This extends to a general theorem: if $\{\operatorname{ran}{f}:f\in\mathbf
C(\mathcal R)\}$ is coinitial in $\mathcal A$ with respect to $\subseteq$,
where $\mathbf C(\mathcal R)=\{f\in(\bigcup\mathcal R)^{\mathcal
R}:R\in\mathcal R\Rightarrow f(R)\in R\}$ collects the choice functions on the
set $\mathcal R$, then $G_1(\mathcal A,\mathcal B)$ and $G_1(\mathcal
R,\neg\mathcal B)$ are dual selection games.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas