Anchored Parallel Repetition for Nonlocal Games

Anchoring games for parallel repetition

Raz's celebrated Parallel Repetition Theorem shows that the probability of simultaneously winning n independent instances of a two-player one-round game G is exponentially small in n, when the maximum success probability of G is less than 1. Though the statement is intuitive, the proof is rather nontrivial and has found important application in hardness of approximation, cryptography, and commu...

Parallel repetition of XOR games

Parallel Repetition of Fortified Games

The Parallel Repetition Theorem upper-bounds the value of a repeated (tensored) two prover game G⊗k in terms of the value of the game G and the number of repetitions k. Contrary to what one might have guessed, the value of G⊗k is not val(G), but rather a more complicated expression depending on properties of G. Indeed, there are numerous works aiming to understand the value of repeated games, b...

Multiplayer Parallel Repetition for Expanding Games

We investigate the value of parallel repetition of one-round games with any number of players k ≥ 2. It has been an open question whether an analogue of Raz’s Parallel Repetition Theorem holds for games with more than two players, i.e., whether the value of the repeated game decays exponentially with the number of repetitions. Verbitsky has shown, via a reduction to the density Hales-Jewett the...

Parallel Repetition of Two Prover Games

The parallel repetition theorem states that for any two-prover game with value smaller than 1, parallel repetition reduces the value of the game in an exponential rate. We give a short introduction to the problem of parallel repetition of two-prover games and some of its applications in theoretical computer science, mathematics and physics. We will concentrate mainly on recent results.