Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evolutionary potential games on lattices   Game theory provides a general mathematical background to study the effect of
pair interactions and evolutionary rules on the macroscopic behavior of
multi-player games where players with a finite number of strategies may
represent a wide scale of biological objects, human individuals, or even their
associations. In these systems the interactions are characterized by matrices
that can be decomposed into elementary matrices (games) and classified into
four types. The concept of decomposition helps the identification of potential
games and also the evaluation of the potential that plays a crucial role in the
determination of the preferred Nash equilibrium, and defines the Boltzmann
distribution towards which these systems evolve for suitable types of dynamical
rules. This survey draws parallel between the potential games and the kinetic
Ising type models which are investigated for a wide scale of connectivity
structures. We discuss briefly the applicability of the tools and concepts of
statistical physics and thermodynamics. Additionally the general features of
ordering phenomena, phase transitions and slow relaxations are outlined and
applied to evolutionary games. The discussion extends to games with three or
more strategies. Finally we discuss what happens when the system is weakly
driven out of the "equilibrium state" by switching on non-potential components
representing games of cyclic dominance.

2
The categories of this paper are: math
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn