Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spontaneous cooperation for public goods   Cooperation for public goods poses a dilemma, where individuals are tempted
to free ride on others' contributions. Classic solutions involve monitoring,
reputation maintenance and costly incentives, but there are important
collective actions based on simple and cheap cues only, for example unplanned
protests and revolts. This can be explained by an Ising model with the
assumption that individuals in uncertain situations tend to conform to the
local majority in their network. Among initial defectors, noise such as rumors
or opponents' provocations causes some of them to cooperate accidentally. At a
critical level of noise, these cooperators trigger a cascade of cooperation. We
find an analytic relationship between the phase transition and the asymmetry of
the Ising model, which in turn reflects the asymmetry of cooperation and
defection. This study thereby shows that in principle, the dilemma of
cooperation can be solved by nothing more than a portion of random noise,
without rational decision making.

2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int