NK Simulation Modeling

NK Simulation Modeling

Lucio Biggiero (University of L'Aquila, Italy & CIRPS, Italy)
DOI: 10.4018/978-1-4666-9770-6.ch002
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Launched and developed primarily by Kauffman from the end of sixties, NK simulation modelling candidates for capturing networks dynamics. Grounded in reference to biological networks, it has aroused a grate and durable interest in economics and management sciences too. This methodology is split into a version focused on studying proper Boolean networks dynamics, whose trajectories are substantially conditioned by Boolean functions, and a (much more frequented) version focused on systems co-evolutionary paths driven by the search for optimizing its fitness value. Besides the unquestionable value of Kauffman's work for the theoretical implications on evolutionary biology and the strong interest for economics and management sciences, in this chapter failures and limitations of both NK modelling versions are discussed. In particular, it is shown that as applications try to be more realistic, this modeling becomes hardly treatable from a computational point of view. On the other hand, it is underlined that, especially the fitness landscape version, NK simulation modelling is very useful to show general aspects of system's dynamics, and the impossibility to find general optima (excepted for very special and unrealistic cases). This result sounds a sharp criticism to general economic equilibrium, and it is perfectly consistent with Simon's contributions.
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A way to perform network dynamic analysis is through Boolean networks (BNs) methodology, which here is treated in one of its most important formulations, proposed by Kauffman in the sixties (1969a, 1969b) and seventies (1971a, 1971b), and then developed and refined in the eighties (1984, 1986, 1988) in two directions: one focused on the self-organizing dynamics followed by a single BN, and the other focused on a system’s (possibly also a BN) potential adaptive evolution within a fitness landscape. BNs theory and modelling is rooted in various research streams developed in the 60s: the theory of dynamic systems (Brian, 1984; Klir, 1991; Weisbuch, 1991; Wuensche, 1994, 1998); automata studies and cellular automata theory (Gill, 1962; Hanson, 2009; Ilachinski, 2001; Shannon & McCarthy, 1953; Sutner, 2009; Trakhtenbrot & Barzin, 1973; Waldrop, 1992; Wolfram, 2002; Wuensche & Lesser, 1992), cybernetics (Ashby, 1956; Ashby & Walker, 19661; Glushkov, 1966; Kauffman, 1984, 1993; Trappl, 1983, von Foerster, 1982, 2003), and complexity science (Arrow et al., 1988; Arthur et al., 1997; Casti, 1989, 2004; Khalil & Boulding, 1996; Mainzer, 1994; Mitleton-Kelly, 2003; Strogatz, 2001, 2003; Sulis & Trofimova, 2000)2. In fact, networks are discrete systems, and so they have much in common with the theory of dynamic systems and complexity science. Further, besides its roots in cybernetics and systems science, cellular automata can be seen as a BN sub-group (Wuensche, 1994). From the same scientific milieu developed in the Santa Fè Institute (Waldrop, 1992), an important stream has been founded and brought forth either in economics (Arrow et al., 1988; Arthur et al., 1997; Arthur, 2010; Blume & Durlauf, 2006; Lane et al., 2009) or in management and organization sciences (McKelvey, 1999, 2004; Schneider & Somers, 2006; and the Special Issue of Organization Science, 1999)3.

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