Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nash Equilibria in Quantum Games   For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The
definition is motivated by a vision of players in game $\G$ communicating via
quantum technology according to a certain standard protocol originally
introduced by Eisert and Wilkins [EW].
  In the game $\G^Q$, each players' strategy set consists of the set of all
probability distributions on the 3-sphere $S^3$. Nash equilibria in this game
can be difficult to compute.
  Our main theorems classify all possible equilibria in $\G^Q$ for a
Zariski-dense set of games $\G$ that we call {\it generic games}. First, we
show that up to a suitable definition of equivalence, any strategy that arises
in equilibrium is supported on at most four points; then we show that those
four points must lie in one of a small number of geometric configurations. One
easy consequence is that for zero-sum games, the payoff to either player in a
mixed strategy quantum equilibrium must equal the average of that player's four
possible payoffs.

19
The categories of this paper are: eess
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an