The Complexity of Equilibria in Cost Sharing Games
- Cite this paper as:
- Syrgkanis V. (2010) The Complexity of Equilibria in Cost Sharing Games. In: Saberi A. (eds) Internet and Network Economics. WINE 2010. Lecture Notes in Computer Science, vol 6484. Springer, Berlin, Heidelberg
We study Congestion Games with non-increasing cost functions (Cost Sharing Games) from a complexity perspective and resolve their computational hardness, which has been an open question. Specifically we prove that when the cost functions have the form f(x) = cr/x (Fair Cost Allocation) then it is PLS-complete to compute a Pure Nash Equilibrium even in the case where strategies of the players are paths on a directed network. For cost functions of the form f(x) = cr(x)/x, where cr(x) is a non-decreasing concave function we also prove PLS-completeness in undirected networks. Thus we extend the results of [7,1] to the non-increasing case. For the case of Matroid Cost Sharing Games, where tractability of Pure Nash Equilibria is known by  we give a greedy polynomial time algorithm that computes a Pure Nash Equilibrium with social cost at most the potential of the optimal strategy profile. Hence, for this class of games we give a polynomial time version of the Potential Method introduced in  for bounding the Price of Stability.
KeywordsCost Sharing PLS-completeness Price of Stability Congestion Games
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