Interactions

During the simulation, firms interact with each other, creating a network of relationships that evolve dynamically due to the continuous creation of new links, removing others and exit from the market of all inefficient firms. The interactions mechanisms modelled in the proposed agent-based system are learning mechanisms and the construction of networks.

In particular, two types of learning mechanisms are considered: the internal learning and the external learning (or relational).

Internal learning considers that the firm produces the knowledge by itself through the skills of individuals who work in it and, therefore, without any interaction with other firms. In the proposed model, the internal learning process has been implemented through the introduction of the “sigmoid function”.

Formally, let ci(t) and (a_ci)(t) respectively the knowledge level in which a firm is specialized and the AC in that specific knowledge, at the time (t + 1) each firm will increase that knowledge level by an amount equal to:

(7) while the knowledge levels in which a firm is not specialized remain unchanged.

External learning is a process of learning by interacting. This process involves the continuous exchange of knowledge between two firms A and B. The external learning occurs only if the condition of complementariness is satisfied, namely if there is at least one category of knowledge in which A dominates B and, at the same time, there is at least one other type of knowledge where B dominates A. As long as there is one category in

which agent A dominates agent B and one in which B dominates A, both agents perceive trade as mutually advantageous and a connection between them is activated.

As reported by Cowan and Jonard (2004), thanks to the external learning process, at every cycle each agent increases the knowledge level in which it is not specialized by an amount proportional to the AC in that knowledge.

Formally, assuming that at time t the firm B dominates the firm A in the category of knowledge ci, the knowledge level that the firm A may reach at time (t + 1) in the category ci, after interacting with the firm B, is expressed by the following relation (symmetric for firm B):

(8)

Instead, as regards the agents representing the contractors and the raw materials suppliers, the increase of knowledge is done through the following relation:

(9)

Another force affecting firms’ knowledge endowment is represented by the obsolescence. In fact, if on one hand every firm keeps on learning during the simulation, on the other hand knowledge levels decrease progressively at each cycle by an amount equal to the obsolescence rate. This latter, modelled through the parameter “obs”, is equal for all firms and is variable in [0, 1].

This phenomenon affects the firms’ survival, causing their death and the exit from the market if they cannot counterbalance this effect through internal or external learning processes.

In order to avoid the exit from the market, each firm searches one or more partners with which create a link and exchange knowledge, in order to maximize its knowledge endowment. Another parameter introduced in the model is the maximum number of interactions that any agent can activate at each cycle. This latter, modeled through the parameter “L”, represents the maximum allowed number of outgoing links. This modelling choice is a reasonable assumption since interaction involves transaction costs; in particular, small firms can manage only a limited number of partners at the same time, though they can build relations with many partners during their life. By limiting the number of simultaneous partners we also force firms to choose among possible partnership alternatives. It is not imposed, however, any constraint on the number of input

links. In the model, the parameter L has been settled equal to 3, as in previous steps of this research (Iandoli et al., 2012) it has been verified that the variation of this parameter in a predefined set of values does not significantly affect the results of simulations.

Figure 2 shows a simplified flow chart describing how firms make decisions about building or breaking links.

Start

Internal learning

Check of links N<L

Look for partners

Check assets complementariness and

past links

External learning (creation of link and knowledge exchange) Break link yes no Stop no yes

Figure 2 – Network building flow-chart

The probability of creating a link is dependent on two elements. The first element is the level of reciprocal complementariness between agents’ knowledge endowment, measured by the following relation:

(10)

where (ci – cj) represents the “cognitive distance” between different specialist skills, while max (ci, cj) is the normalization factor. The second element influencing the probability of link establishment between two firms is the (normalized) number of links that they have already established in the past. In fact, one of our objective has been to introduce a mechanism of selection that takes into account whether and how the “embeddedness” of the firms in the social system can influence their behavior and, ultimately, as the latter may reflect on the network characteristics. In this regard, when a firm chooses to develop cooperative relationships with other entities, it selects its partners

based on reputations, recommendations or relying on previous experiences were successful.

Firms that prefer previous partners are driven by a sort of “inertial rationality”. However, the embeddedness in the social system does not prevent the actors in the system to make decisions based solely on an “utilitarian rationality”, mainly in order to complement their knowledge endowment and thus enable collaboration, even sporadic, with entities other than the partner usually involved in exchange relationships.

More in depth, we have modelled the probability for a firm to establish a link with a potential partner (when the complementariness condition is satisfied) in the following way:

(11)

where x represents the number of links established in the past between the two firms, y represents the knowledge gap between different specialist skills, while the T parameter measures the relative weight of these two variables and can assume values in the range [0,1]. From this relation we deduce that for high values of T, the probability that two firms establish a link depends more on the number of relationships that they have already established in the past, while for low values of T such probability depends to greater extent from their cognitive gap.