Stackelberg Strategies and Collusion in Network Games with Splittable Flow

  • Authors:

  • Tobias Harks

  • Affiliations:

  • Institute of Mathematics, Technical University, Berlin, Germany

  • Venue:
  • Approximation and Online Algorithms
  • Year:
  • 2009

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Abstract

We study the impact of collusion in network games with splittable flow and focus on the well established price of anarchy as a measure of this impact. We first investigate symmetric load balancing games and show that the price of anarchy is bounded from above by m , where m denotes the number of coalitions. For general networks, we present an instance showing that the price of anarchy is unbounded, even in the case of two coalitions. If latencies are restricted to polynomials, we prove upper bounds on the price of anarchy for general networks, which improve upon the current best ones except for affine latencies. In light of the negative results even for two coalitions, we analyze the effectiveness of Stackelberg strategies as a means to improve the quality of Nash equilibria. We show that for a simple strategy, called SCALE, the price of anarchy reduces to 1 + α for general networks and a single atomic follower. Finally, we investigate SCALE for multiple coalitional followers, general networks, and affine linear latencies. We present the first known upper bound on the price of anarchy in this case. Our bound smoothly varies between 1.5 when α= 0 and full efficiency when α= 1.