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Raz's parallel repetition theorem together with improvements of Holenstein shows that for any two-prover one-round game with value at most 1 - ∈ (for ∈ ≤ 1/2), the value of the game repeated n times in parallel on independent inputs is at most (1-∈)Ω(∈2n/ℓ) where ℓ is the answer length of the game. For free games (which are games in which the inputs to the two players are uniform and independent)...
This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdzinski. First, we informally show which structures are difficult to solve for the algorithm. Second, we outline a family of games on which the algorithm requires exponentially many strategy iterations, answering in the negative the long-standing question whether this...
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