The price of anarchy in selfish multicast routing

• Authors: Andreas Baltz;Sandro Esquivel;Lasse Kliemann;Anand Srivastav
• Venue: CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
• Year: 2006

We study the price of anarchy for selfish multicast routing games in directed multigraphs with latency functions on the edges, extending the known theory for the unicast situation, and exhibiting new phenomena not present in the unicast model. In the multicast model we have N commodities (or player classes), where for each $ i=1,\hdots,N$, a flow from a source si to a finite number of terminals $t_i^1,\hdots,t_i^{k_i}$ has to be routed such that every terminal tij receives flow ni∈ℝ≥0. One of the significant results of this paper are upper and lower bounds on the price of anarchy for edge latencies being polynomials of degree at most p with non-negative coefficients. We show an upper bound of $(p+1)\cdot\frac{\nu^{p+1}}{\nu^*}$ in some variants of multicast routing. We also prove a lower bound of νp, so we have upper and lower bounds that are tight up to a factor of (p+1)ν. Here, ν and ν* are network and strategy dependent parameters reflecting the maximum/minimum consumption of the network. Both are 1 in the unicast case. Our lower bound of νp, where in the general situation we have ν1, shows an exponential increase compared to the Roughgarden bound of O(p/lnp) for the unicast model. This exhibits the contrast to the unicast case, where we have Roughgarden’s (2002) result that the price of anarchy is independent of the network topology. To our knowledge this paper is the first thorough study of the price of anarchy in the multicast scenario. The approach may lead to further research extending game-theoretic network analysis to models used in applications.