SOME NOTES ON COMPUTATION OF GAMES SOLUTIONS

By G. Brown. 1949

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Citations in the corpus

Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness (2017, methodology): “than using a no-regret dynamic, we instead use a simple iterative procedure known as Fictitious Play (Brown, 1949).”
Introduction to Multi-Armed Bandits (2019, background): “-player zero-sum games where each player bestresponds to the empirical play of the opponent (i.e., the historical frequency distribution over the arms). CHAPTER 9. BANDITS AND GAMES 111 Introduced in Brown (1949), ﬁctitious play was proved to converge at the rate O(t 1=n) for n ngame matrices (Robin”
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games (2019, methodology): “There, αm are adapted processes to the filtration generated by Brownian motions, i.e. one can intuitively think αm as functions of W[0,T ], thus do not change as strategies/states vary, as long as the training paths of W are fixed. Therefore, using α−i,m only requires constant memory, since one can ”
AN ITERATIVE METHOD OF SOLVING A GAME (1951, background): “In this notation, (1) can be rewritten as follows: (2) min EA .”
From Nash and Brown to Maynard Smith: Equilibria, Dynamics and ESS (2001, background): “With a different interpretation as a learning process, but in a mathematically equivalent form, the best response dynamics was already introduced as fictitious play by Brown (1949, 1951).”
A Counter-example to Karlin's Strong Conjecture for Fictitious Play (2014, methodology): “So, after exchanging the strategies1 ↔ 2, we can repeat the players’ choices at Steps3, 4, 5 and6 in Steps7, 8, 9 and10 respectively to arrive atU(10) = [5, 5] andV (10) = [4, 6].”