Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evolutionary Game Theory Squared: Evolving Agents in Endogenously
  Evolving Zero-Sum Games   The predominant paradigm in evolutionary game theory and more generally
online learning in games is based on a clear distinction between a population
of dynamic agents that interact given a fixed, static game. In this paper, we
move away from the artificial divide between dynamic agents and static games,
to introduce and analyze a large class of competitive settings where both the
agents and the games they play evolve strategically over time. We focus on
arguably the most archetypal game-theoretic setting -- zero-sum games (as well
as network generalizations) -- and the most studied evolutionary learning
dynamic -- replicator, the continuous-time analogue of multiplicative weights.
Populations of agents compete against each other in a zero-sum competition that
itself evolves adversarially to the current population mixture. Remarkably,
despite the chaotic coevolution of agents and games, we prove that the system
exhibits a number of regularities. First, the system has conservation laws of
an information-theoretic flavor that couple the behavior of all agents and
games. Secondly, the system is Poincar\'{e} recurrent, with effectively all
possible initializations of agents and games lying on recurrent orbits that
come arbitrarily close to their initial conditions infinitely often. Thirdly,
the time-average agent behavior and utility converge to the Nash equilibrium
values of the time-average game. Finally, we provide a polynomial time
algorithm to efficiently predict this time-average behavior for any such
coevolving network game.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin