Lecture 2 : Minimax theorem , Impagliazzo Hard Core Lemma
نویسنده
چکیده
Zero-sum games are two player games played on a matrix M ∈ Matm×n(R). The row player, denoted R, chooses a row i ∈ [m] and the column player C chooses a column j ∈ [n], simultaneously. The payoff to the row player is Mij and the payoff to the column player is −Mij (hence the game is “zero-sum”). We can also consider randomized strategies, where R chooses a probability distribution p on [m], which can be written as a vector in Rm, and the column player chooses a probability distribution q on Rn. The expected payoff to the row player, denoted E(p, q), is thus equal to pMq = ∑
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