Complex Systems, Agent Cognition and Network Structure : Modeling with Low Cognition Agents Rich Colbaugh, Kristin Glass, Paul Ormerod and Bridget Rosewell May 2005

Type of theoryAbility of agents Ability of agent to gather informationto process information Rationalfullmaximize Bounded rationalpartialmaximize Behavioralpartialrule of thumb

If robustness and evolvability are both important: system sensitivity to variations in topology increases as system maturity increases; system sensitivity to variations in vertex characteristics decreases as system maturity increases. This result suggests that as complex systems “mature”, the importance of accurately modeling their vertex characteristics decreases i.e. The relevant topology of the system is more important than the specific behavioral rules of agents Fundamentals of complex systems

Zero intelligence traders in financial markets (Farmer/Patelli/Zovko 2003) Motivating examples Problem: explore extent to which constraints imposed by market institutions can explain financial market behavior. Model: agents submit trade orders at random (subject only to a budget constraint) Result: model reproduces “stylized facts” of London Stock Exchange (e.g., bid-ask spread, price diffusion, market impact function).

Information Cascades (Watts 2002) Problem: small initial shocks can cascade to affect or disrupt large systems that have proved stable with respect to similar disturbances in the past e.g. financial markets Motivating examples Model: network of agents whose decisions are determined by actions of neighbours according to a simple threshold rule Result:2 regimes are identified in which very large cascades occur very rarely. When cascade propagation is limited by the connectivity of the network, a power law distribution of cascades is observed. When the network is highly connected, the distribution is bimodal, exponential at small cascade size with a second peak at the size of the system i.e. a global cascade

Economic Recessions (Ormerod 2004) Problem: investigate cumulative size distribution of economic recessions under capitalism, Model: optimism and pessimism are transmitted across a highly connected network of firms via a threshold rule Motivating Examples Result: no matter how the data are partitioned, the null hypothesis that cumulative size distribution is exponential is never rejected at p = Qualitatively, however, there is an exponential fit to the bulk of the data, with a second peak describing a small number of very large recessions. Model gives a good approximation to this

Economic Recessions (Ormerod 2002) Problem: economics lacks a satisfactory theory of the business cycle, and existing models cannot replicate the time and frequency domain properties of the data Motivating Examples Model: firms form views on optimism/pessimism on a strongly connected network by observing just the previous year’s rate of growth of GDP. Optimism determines GDP growth this year Result: time and frequency domain properties of data replicated, as are the cross- correlations of agent/sector output growth (the key feature of the cycle: Lucas 1977). Model also replicates cumulative size distribution of recessions very accurately.

Metadata analysis of social networks (Colbaugh/Glass 2002) Problem: use metadata analysis to understand organization behavior. Model: agents exchange information according to simple rules but over realistic social networks. Result: metadata analysis yields identification of collaborating and “important” agents. Motivating examples

Low cognition firms (Ormerod/Rosewell 2003) Problem: determine degree to which firms are able to “learn” about how best to compete/ cooperate with other firms. Model: interacting network of firms which have either some or no capacity for learning. Result: “no learning” model reproduces the stylized facts of firm extinction (frequency/size probability distribution and relationship between firm age and extinction probability). Motivating examples

Low foresight criminals (Ormerod/Colbaugh/Glass 2004): Problem: investigate degree to which criminal behavior is explained by “low foresight” agent models. Model: criminals face increased crime opportunities as they gain experience but do not anticipate consequences of their actions. Result: low foresight model reproduces stylized facts of criminal behavior (e.g., probability distribution for crimes per agent). Motivating examples

Main result Preceding results suggest potential utility of low cognition agent models: empirical evidence demonstrates that such models are able to capture important aspects of several “real world” social systems; complex systems theory suggests that social systems may evolve so that the topology/protocols governing agent interaction strongly constrains system behavior, providing robustness and evolvability in the face of wide variations in agents’ information resources and strategies/capabilities for information processing.