Minimizing Rosenthal Potential in Multicast Games
A multicast game is a network design game modelling how selfish non-cooperative agents build and maintain one-to-many network communication. There is a special source node and a collection of agents located at corresponding terminals. Each agent is interested in selecting a route from the special source to its terminal minimizing the cost. The mutual influence of the agents is determined by a cost sharing mechanism, which evenly splits the cost of an edge among all the agents using it for routing. The existence of a Nash equilibrium for the game was previously established by the means of Rosenthal potential. Anshelevich et al. [FOCS 2004, SICOMP 2008] introduced a measure of quality of the best Nash equilibrium, the price of stability, as the ratio of its cost to the optimum network cost. While Rosenthal potential is a reasonable measure of the quality of Nash equilibra, finding a Nash equilibrium minimizing this potential is NP-hard.
For a given strategy profile s and integer k ≥ 1, there is a local search algorithm which in time n O(k) ·|G| O(1) finds a better strategy profile, if there is any, in a k-exchange neighbourhood of s. In other words, the algorithm decides if Rosenthal potential can be decreased by changing strategies of at most k agents;
The running time of our local search algorithm is essentially tight: unless FPT = W, for any function f(k), searching of the k-neighbourhood cannot be done in time f(k)·|G| O(1).
KeywordsNash Equilibrium Local Search Cost Sharing Local Search Algorithm Social Optimum
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