Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Structure of N-Player Games when Influence and Independence Collide   We study the mathematical properties of probabilistic processes in which the
independent actions of $n$ players (`causes') can influence the outcome of each
player (`effects'). In such a setting, each pair of outcomes will generally be
statistically correlated, even if the actions of all the players provide a
complete causal description of the players' outcomes, and even if we condition
on the outcome of any one player's action. This correlation always holds when
$n=2$, but when $n=3$ there exists a highly symmetric process, recently
studied, in which each cause can influence each effect, and yet each pair of
effects is probabilistically independent (even upon conditioning on any one
cause). We study such symmetric processes in more detail, obtaining a complete
classification for all $n \geq 3$. Using a variety of mathematical techniques,
we describe the geometry and topology of the underlying probability space that
allows independence and influence to coexist.

1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga