1 research outputs found
The Game-Theoretic Formation of Interconnections Between Networks
We introduce a network design game where the objective of the players is to
design the interconnections between the nodes of two different networks
and in order to maximize certain local utility functions. In this
setting, each player is associated with a node in and has functional
dependencies on certain nodes in . We use a distance-based utility for the
players in which the goal of each player is to purchase a set of edges
(incident to its associated node) such that the sum of the distances between
its associated node and the nodes it depends on in is minimized. We
consider a heterogeneous set of players (i.e., players have their own costs and
benefits for constructing edges). We show that finding a best response of a
player in this game is NP-hard. Despite this, we characterize some properties
of the best response actions which are helpful in determining a Nash
equilibrium for certain instances of this game. In particular, we prove
existence of pure Nash equilibria in this game when contains a star
subgraph, and provide an algorithm that outputs such an equilibrium for any set
of players. Finally, we show that the price of anarchy in this game can be
arbitrarily large