2014/04 | LEM Working Paper Series | |
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The arrival of the new |
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Luigi Marengo, Paolo Zeppini |
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Abstract | ||
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In this work we present a number of urn models in which, contrary to standard
Polya urns, the number of competing alternatives is not given from the outset but
may increase with the arrival of innovations. We begin by describing a variant
of Polya urns, first introduced by Fred Hoppe, in which balls of previously non
existing colours are added with some (declining) probability. We then propose new
variants in which the probability of the arrival on new colours is itself subject to
adaptive change depending on the success of past innovations. We numerically
simulate different specifications of these urns with adaptively changing mutation
rate and show that they can account for complex patterns of evolution in which
periods of exploration with clusters of innovations are followed by periods in which
the dynamics of the system is driven by selection among a stable set of alternatives.
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