Parallel repetition of the odd cycle game

Abstract

Higher powers of the Odd Cycle Game has been the focus of recent investigations [3,4]. In [4] it was shown that if we repeat the game d times in parallel, the winning probability is upper bounded by , when d∈=∈n 2logn. We 1 Determine the exact value of the square of the game; 1 Show that if Alice and Bob are allowed to communicate a few bits they have a strategy with greatly increased winning probability; 1 Develop a new metric conjectured to give the precise value of the game up-to second order precision in 1/n for constant d. 1 Show an 1∈-∈Ω(d/nlogn) upper bound for d∈=∈nlogn if one player uses a "symmetric" strategy. © 2008 Springer-Verlag Berlin Heidelberg.