@MISC{Huang_collusionin, author = {Chien-Chung Huang}, title = {Collusion in Atomic Splittable Routing Games}, year = {} }

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Abstract

We investigate how collusion affects the social cost in atomic splittable routing games. Suppose that players form coalitions and each coalition behaves as if it were a single player controlling all the flows of its participants. It may be tempting to conjecture that the social cost would be lower after collusion, since there would be more coordination among the players. We construct examples to show that this conjecture is not true. Even in very simple single-source-single-destination networks, the social cost of the post-collusion equilibrium can be higher than that of the pre-collusion equilibrium. This counter-intuitive phenomenon of collusion prompts us to ask the question: under what conditions would the social cost of the post-collusion equilibrium be bounded by the social cost of the pre-collusion equilibrium? We show that if (i) the network is “well-designed ” (satisfying a natural condition), and (ii) the delay functions are affine, then collusion is always beneficial for the social cost in the Nash equilibria. On the other hand, if either of the above conditions is unsatisfied, collusion can worsen the social cost. Our main technique is a novel flow-augmenting algorithm to build Nash equilibria. Our positive result for collusion is obtained by applying this algorithm simultaneously to two different flow value profiles of players and observing the difference in the derivatives of their social costs. Moreover, for a non-trivial subclass of selfish routing games, this algorithm finds the exact Nash equilibrium in polynomial time.