Chapter 3: Computational and Dynamic Complexity in Economics
J. Barkley Rosser, Jr.* 3.1 Introduction As reported by Horgan (1997, p. 305), Seth Lloyd has gathered at least 45 definitions of complexity. Rosser (1999) argued for the usefulness in studying economics of a definition he called dynamic complexity that was originated by Day (1994). This is that a dynamical economic system fails to generate convergence to a point, a limit cycle, or an explosion (or implosion) endogenously from its deterministic parts. It was argued that nonlinearity was a necessary but not sufficient condition for this form of complexity,1 and that this definition constituted a suitably broad “big tent” to encompass the “four Cs” of cybernetics, catastrophe, chaos, and “small tent” (or heterogeneous agents) complexity. Other approaches used in economics have included structural (Pryor, 1995; Stodder, 1995),2 hierarchical (Simon, 1962), and computational (Lewis, 1985; Albin with Foley, 1998; Velupillai, 2000). In recent years (Markose, 2005; Velupillai, 2005a, b, c) there has been a tendency to argue that the latter concept is superior because of its foundation on more well-defined ideas, such as algorithmic complexity (Chaitin, 1987) and stochastic complexity (Rissanen, 1989, 2005). These are seen as founded more deeply on work of Shannon (1948) and Kolmogorov (1983). Mirowski (2007) argues that markets themselves should be seen as algorithms that are evolving to higher levels in a Chomskyian (1959) hierarchy of computational systems, especially as they increasingly are carried over computers and become resolved through programmed double-auction systems and the like. McCauley (2004, 2005) and Israel (2005) argue that...
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