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SUMMARY:On a mean field model for knowledge growth - Wolfram\, M-T (Austri
 an Academy of Sciences)
DTSTART:20141008T150000Z
DTEND:20141008T153000Z
UID:TALK55026@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Lucas and Moll proposed a  mean field model for knowledge grow
 th\, in which individuals can split their time between producing goods wit
 h their knowledge or increasing their knowledge level by meeting other ind
 ividuals. These meetings are modeled by 'collisions'\, in which knowledge 
 is exchanged. Hence the  evolution of the knowledge distribution can by de
 scribed by a Boltzmann type equation. The choice of how much  time is spen
 d on learning or producing goods\, is determined by the overall production
  level. The resulting mean field  model corresponds to an optimal control 
 problem with a Boltzmann type constraint. We present first analytic result
 s and discuss the existence of special equilibrium solutions. Furthermore 
 we illustrate the behaviour of the model with numerical simulations.\n
LOCATION:Seminar Room 1\, Newton Institute
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