2,191 research outputs found
Payoff Performance of Fictitious Play
We investigate how well continuous-time fictitious play in two-player games
performs in terms of average payoff, particularly compared to Nash equilibrium
payoff. We show that in many games, fictitious play outperforms Nash
equilibrium on average or even at all times, and moreover that any game is
linearly equivalent to one in which this is the case. Conversely, we provide
conditions under which Nash equilibrium payoff dominates fictitious play
payoff. A key step in our analysis is to show that fictitious play dynamics
asymptotically converges the set of coarse correlated equilibria (a fact which
is implicit in the literature).Comment: 16 pages, 4 figure
Consistency of vanishing smooth fictitious play
We discuss consistency of Vanishing Smooth Fictitious Play, a strategy in the
context of game theory, which can be regarded as a smooth fictitious play
procedure, where the smoothing parameter is time-dependent and asymptotically
vanishes. This answers a question initially raised by Drew Fudenberg and Satoru
Takahashi.Comment: 17 page
No-regret Dynamics and Fictitious Play
Potential based no-regret dynamics are shown to be related to fictitious
play. Roughly, these are epsilon-best reply dynamics where epsilon is the
maximal regret, which vanishes with time. This allows for alternative and
sometimes much shorter proofs of known results on convergence of no-regret
dynamics to the set of Nash equilibria
Fictitious play and- no-cycling conditions
We investigate the paths of pure strategy profiles induced by the fictitious play process. We present rules that such paths must follow. Using these rules we prove that every non-degenerate 2*3 game has the continuous fictitious play property, that is, every continuous fictitious play process, independent of initial actions and beliefs, approaches equilibrium in such games.
Naive fictitious play in an evolutionary environment
A fictitious play algorithm with a unit memory length within an
evolutionary environment is considered. The aggregate average behavior
model is proposed and analyzed. The existence, uniqueness and
global asymptotic stability of equilibrium is proved for games with a
cycling property. Also, a noisy version of the algorithm is considered,
which gives rise to a system with a unique, globally asymptotically
stable equilibrium for any game
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