Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nash equilibria in Voronoi games on graphs   In this paper we study a game where every player is to choose a vertex
(facility) in a given undirected graph. All vertices (customers) are then
assigned to closest facilities and a player's payoff is the number of customers
assigned to it. We show that deciding the existence of a Nash equilibrium for a
given graph is NP-hard which to our knowledge is the first result of this kind
for a zero-sum game. We also introduce a new measure, the social cost
discrepancy, defined as the ratio of the costs between the worst and the best
Nash equilibria. We show that the social cost discrepancy in our game is
Omega(sqrt(n/k)) and O(sqrt(kn)), where n is the number of vertices and k the
number of players.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph