Complex Systems vs. Simplex Systems:the behaviour of collectivities following the Combinatory System view

In Agent-Based Models, collectivities are normally interpreted as complex (adaptive) systems, defined as a plurality of (usually large) blind (reactive) or intelligent (active) specialized (usually strongly) interacting agents (or processes), whose collective macro behaviour - determined by the interaction of the micro behaviours of the agents - is non-linear and derives from local (proximity) rules following a schema (innate or learned). My paper also aims to demonstrate that collectivities whose agents show a similar nature or significance, develop analogous micro behaviours which produce analogous effects and are not (necessarily) interconnected can produce a complex (self-organized or even chaotic and, of course, path-dependent) macro behaviour: the accumulation of objects, the spread of features or information and the pursuit or exceeding of a limit. I have provocatively defined these collectivities as simplex systems, since the similarity of the agents and the micro behaviours, and the absence of direct interactions among the agents, make these collectivities a particular simplified class of complex (adaptive) systems as usually conceived. When simplex systems show a micro-macro feedback between micro and macro behaviours, they can then be viewed as Combinatory Systems. The second aim of this research paper is to illustrate, in particular – with the aid of a combinatory lattice – the systems of improvement and progress, whose effect is to produce progress in the overall state of a simplex system in which the agents pursue their search for individual improvement, as we can typically observe in collectivities of economic agents moved by their own interests or objectives in a local and global context.