We study the performance of non cooperative
networks in light of three major topology design considerations, namely the
price of establishing a link, path delay, and path proneness to congestion, the
latter being modeled through the “relaying extent” of the nodes. We analyze
these considerations and the tradeoffs between them from a game-theoretic
perspective, where each network element attempts to optimize its individual
performance. We show that for all considered cases but one, the existence of a
Nash equilibrium point is guaranteed. For the latter case, we indicate, by
simulations, that practical scenarios tend to admit Nash equilibrium. In
addition, we demonstrate that the price of anarchy, i.e., the performance
penalty incurred by non cooperative behavior, may be prohibitively large; yet,
we also show that such games usually admit at least one Nash equilibrium that
is system-wide optimal, i.e., their price of stability is 1. This finding
suggests that a major improvement can be achieved by providing a central
(“social”) agent with the ability to impose the initial configuration on the
system.
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