Additional paragraphs:
In this Feature we have desisted from putting up straw men of conventional economics ( ‘the rational economic man’ and the ‘representative agent’[1] being the much maligned ones) and then proceeding to tear them down in an unedifying manner. Instead, the Feature articles have worked to provide detailed insights and examples of both the challenges and the prospects for Economics that are offered by the new methods of the complexity sciences. This overview underscores the principle that the applicability or not of the static optimization framework of conventional economics depends on the domain of the problem and in particular gives the modern theories behind non-computability issues. Table 1 in the overview summarises the way in which the methods of conventional economics and econometrics are limited in scope with regard to the type of problems it can give valid analysis for and how the mathematics of incompleteness and adaptive methods of computation and agent based simulations are needed to understand and model a whole swathe of economic phenomena which are anomalies in the conventional economics framework. These include innovation, competitive co-evolution, persistent heterogeneity, increasing returns, the error driven processes behind market equilibria, herding, crashes and extreme events such as in the business cycle or in stock markets. Such a list is ofcourse by no means exhaustive. While many of these issues have been discussed in the ACE fraternity (some of which are reviewed here), this Feature attempts to rectify a lack of discussion on the distinction between self-organized systems that can and cannot produce ‘new forms’ by highlighting the non-trivial dynamic of adaptive novelty production. The rest of the paper is structured as follows.
We argued that mathematically, problems involving strongly self-referential global/ system wide mappings, like an endogenously determined price or reward system, or those that involve coevolutionary contrarian or hostile agents make these impossible to be solved by deductive means of Column I, Table 1. Adaptive/evolutionary methods of Column III, Table 1 have to be used and models beyond optimization and the rational economic man of neoclassical economics are needed . The computability foundations and use of constructive agent based models have opened up a new branch of ‘computational mechanism design’ which utilizes principles of self-organisation or artificially evolved solutions to implement in the design of markets. This will, however, take us beyond the remit of this Feature.
[1] See, Kirman (1992) for a useful critique on how the representative agent model assumes away the complexities of markets with many agents often with conflicting interests and partial information.