Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real World Games Look Like Spinning Tops   This paper investigates the geometrical properties of real world games (e.g.
Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure
resemble a spinning top, with the upright axis representing transitive
strength, and the radial axis, which corresponds to the number of cycles that
exist at a particular transitive strength, representing the non-transitive
dimension. We prove the existence of this geometry for a wide class of real
world games, exposing their temporal nature. Additionally, we show that this
unique structure also has consequences for learning - it clarifies why
populations of strategies are necessary for training of agents, and how
population size relates to the structure of the game. Finally, we empirically
validate these claims by using a selection of nine real world two-player
zero-sum symmetric games, showing 1) the spinning top structure is revealed and
can be easily re-constructed by using a new method of Nash clustering to
measure the interaction between transitive and cyclical strategy behaviour, and
2) the effect that population size has on the convergence in these games.

25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg