Obviously, the number of agents in each group and the degree of agents change dynamically as the network evolves.
Hereafter the in/out-degree correlation can be roughly identified with parameter (alpha ) when (alpha in [0,1]) as an increase in such parameter corresponds with an increase in the similarity between the out-degree and in-degree of agents.
Setting aside peculiarly moral reasons, common sense suggests that ordinary practical reasons exhibit a high degree of agent-relativity.
In addition, convergence theorems guarantee that, as long as novel evidence keeps coming in, the degrees of belief of agents with very different initial attitudes will finally converge (Gaifman and Snir 1982).
Moreover, by introducing DSC technology, it avoids the well known problem of 'explosion of complexity' that conventional backstepping method suffers from along with the increasement of the degree of individual agents.
We measure agent-to-agent ties by preference correlation using the contribution degree of one agent to another and the preference similarity degree between two agents.
If, instead, (alpha =1) then an agent with twice the out-degree of another agent is selected twice as often.
Instead, since discrete spaces are implemented as directed networks, competitiveness corresponds to the out-degree of each agent, i.e., to the number of arrows starting from the considered agent and directed to those agents it wants to face.
Following that, as an important innovation, confidence level is introduced to quantify the degree of the agent's risk aversion, and the effects of the agent's attitude toward risk on the optimal contract and the principal's income are taken into account.
ABM provides a natural description of a system that can be calibrated and validated by representative expert agents, and is flexible enough to be tuned to high degrees of sensitivity in agent behaviours and interactions.
