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Unformatted text preview: 14.127 Lecture 7 Xavier Gabaix March 18, 2004 1 Learning in games • Drew Fudenberg and David Levine, The Theory of Learning in Games 1.1 Fictitious play Let γ denotes frequencies of i ’s opponents play i t • number of times s − was played till i now γ ( s − i i t ) = t γ i t Player i plays the best response BR • • Big concerns: — Asymptotic behavior: do we converge or do we cycle? — If we converge, then to what subset of Nash equilibria? • Caveat. Empirical distribution need not converge 1.2 Replicator dynamics • Call θ s i i t = fraction of players of type i who play s i . • Postulate dynamics — In discrete time θ vector +1 θ +1 i t i t ( s 1 ) , ..., θ +1 i t ( s n ) = θ vector i t i t θ vector − i t − θ vector + λ BR = — In continuous time d θ vector +1 i t i t i t θ vector − − θ vector = λ BR dt • Then analyze the dynamics: chaos, cycles, fixed points 1.3 Experience weighted attraction model, EWA • CamererHo, Econometrica 1999 • Denote N t = number of “observation equivalent”...
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This note was uploaded on 12/26/2011 for the course ECON 14.127 taught by Professor Staff during the Fall '10 term at MIT.
 Fall '10
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