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The model of emergent innovation networks of Cowan, Jonard and Zimmermann
[6] (CJZ) also simulates a population of firms with knowledge resources. Each firm's
knowledge is a vector of continuous variables, representing several dimensions of
knowledge. Pairs of firms can collaborate to create new amounts of knowledge, with
the amount computed using a constant-elasticity-of-substitution (CES) production
function. Each input to this function is a weighted sum of the minimum and maximum
values in the corresponding dimension of the collaborating firms' knowledge vectors,
the idea here being that if knowledge in each dimension is largely independent of the
other dimensions, knowledge is decomposable into subtasks, and firms will be able to
choose the best knowledge value for each subtask, but with interdependent knowledge
dimensions, both firms may be held back by the weakest firm. If collaboration is by
chance successful, the amount output from the production function will be added to
one of the variables in a participant's knowledge vector. Evaluating potential collabo-
ration partners is based on experience of recent success, including the evaluating
firm's direct experience of the candidate partner (relational credit), and also the
evaluator's indirect experience obtained from its other recent collaborators (structural
credit). Once all firms have evaluated each other, a set of partnerships is formed using
the algorithm for the roommate matching problem. Data on partnerships can be used
to draw an innovation network of firms. The structural properties of this network can
then be related to the main parameters, the weighting between collaborating firms'
minimum and maximum knowledge inputs (representing the decomposability of
knowledge) and the weighting between relational and structural credit.
Padgett's hypercycles model of economic production [7, 29, 30] draws upon the
ideas from theoretical biology of hypercycles and auto-catalysis [25]. It simulates a
population of firms engaged in the transformation and transfer of products. Each firm
begins with randomly chosen production skills, called production rules. Inspired by
Fontana's algorithmic chemistry these are of the form: given a product of type x,
transform it into an output of type y. Each time step a new production run attempt is
simulated. A product of a random type is drawn from a common environment by one
randomly chosen firm and transformed using one of that firm's rules. The output
product from transformation is then transferred to a randomly chosen neighbour in a
grid network of firms. If a firm lacks a rule suitable for transforming the product it has
received, then the product is dumped into the environment and the production run
ends. Otherwise, the firm uses a compatible rule to transform it and transfers the out-
put to one of its neighbours, and the production run continues. In addition to proc-
esses of transformation and transfer, firms learn by doing. Whenever two firms in
succession in the production run have compatible rules to transform products, one of
the firms increases its stock of instances of the rule it has just used. Meanwhile, under
a process of rule decay, somewhere in the population of firms a randomly chosen rule
is forgotten. Firms that forget all their rules exit the system, leaving gaps in the net-
work. The effect of these four processes (product transformation and transferral, and
rule learning by doing and rule decay) is that under various parameter settings a self-
maintaining system of firms and rules can emerge over time through self-
organisation. This system depends upon there being hypercycles of rules, in which
constituent rules are all supplied by other constituent rules.
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