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Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games

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2 Author(s)
Daskalakis, C. ; Berkeley Comput. Sci., Univ. of California, Berkeley, CA ; Papadimitriou, Christos H.

We show that there is a polynomial-time approximation scheme for computing Nash equilibria in anonymous games with any fixed number of strategies (a very broad and important class of games), extending the two-strategy result of Daskalakis and Papadimitriou 2007. The approximation guarantee follows from a probabilistic result of more general interest: The distribution of the sum of n independent unit vectors with values ranging over {e1,...,ek}, where ei is the unit vector along dimension i of the k-dimensional Euclidean space, can be approximated by the distribution of the sum of another set of independent unit vectors whose probabilities of obtaining each value are multiples of 1/z for some integer z, and so that the variational distance of the two distributions is at most eps, where eps is bounded by an inverse polynomial in z and a function of k, but with no dependence on n. Our probabilistic result specifies the construction of a surprisingly sparse epsi-cover- under the total variation distance - of the set of distributions of sums of independent unit vectors, which is of interest on its own right.

Published in:

Foundations of Computer Science, 2008. FOCS '08. IEEE 49th Annual IEEE Symposium on

Date of Conference:

25-28 Oct. 2008