An Iterative Method of Solving a Game

Belief Affirming in Learning Processes

“…This simple theorem is enough to guarantee that, in zero-sum two-player games, fictitious play is always belief affirming. The convergence of fictitious play in such games was proved by Robinson [13]. We show, moreover, that the average payoff converges to the value of the game.…”

Rage Against the Machines: How Subjects Learn to Play Against Computers

“…A second decision rule that is studied extensively in the literature is fictitious play (see Brown, 1951, Robinson, 1951, and Fudenberg and Levine, 1998, chapter 2). A player who uses fictitious play chooses in each round a myopic best response against the historical frequency of his opponent's actions (amended by an initial weight for each action).…”

Evolution of Beliefs and the Nash Equilibrium of Normal Form Games

“…11 Note that it is a path-by-path property. Proposition 1 states that if both players' assessment rules are adaptive, then any point of convergence in beliefs corresponds to a Nash equilibrium of the game G. Proposition 1.…”

“…0098 Figure 1 We know from the theorem by Robinson [11] 1 that the sequence of each player's beliefs converges to 0.5H+0.5T, which corresponds to the Nash equilibrium of the game. Figure 2 illustrates the locus of converging beliefs as a spiral around the Nash equilibrium point.…”

“…First introduced by Brown [1], fictitious play and its generalization have been extensively studied as models of learning in recent years. Robinson [11] proves that fictitious play converges to a Nash equilibrium in any zero-sum games. Miyasawa [9] proves the same in 2_2 games.…”