14127lec7_l_in_g

14127lec7_l_in_g - 14.127 Lecture 7 Xavier Gabaix 1...

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14.127 Lecture 7 Xavier Gabaix March 18, 2004
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1 Learning in games Drew Fudenberg and David Levine, The Theory of Learning in Games
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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
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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
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1.3 Experience weighted attraction model, EWA Camerer-Ho, Econometrica 1999 Denote N t = number of “observation equivalent” past responses such that N t +1 = ρN t + 1
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