Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz Continuity and Approximate Equilibria   In this paper, we study games with continuous action spaces and non-linear
payoff functions. Our key insight is that Lipschitz continuity of the payoff
function allows us to provide algorithms for finding approximate equilibria in
these games. We begin by studying Lipschitz games, which encompass, for
example, all concave games with Lipschitz continuous payoff functions. We
provide an efficient algorithm for computing approximate equilibria in these
games. Then we turn our attention to penalty games, which encompass biased
games and games in which players take risk into account. Here we show that if
the penalty function is Lipschitz continuous, then we can provide a
quasi-polynomial time approximation scheme. Finally, we study distance biased
games, where we present simple strongly polynomial time algorithms for finding
best responses in $L_1$, $L_2^2$, and $L_\infty$ biased games, and then use
these algorithms to provide strongly polynomial algorithms that find $2/3$,
$5/7$, and $2/3$ approximations for these norms, respectively.

24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph