Complexity Studies in Economics Bruno Gaminha -­‐ [email protected] -­‐ S5 -­‐ 327/1 Jorge Louçã -­‐ [email protected] The structure of interacJon I.  Cellular automaton II.  MulJ-­‐agent simulaJon III.  SJgmergic systems IV.  Network Theory The structure of interacJon -­‐ Cellular Automaton A cellular automaton consists: • 
• 
• 
• 
• 
• 
• 
regular grid of cells. each cell or grid is in one of a finite number of states, such as on and off. the grid can be in any finite number of dimensions. for each cell, a set of cells called its neighbourhood is defined relaJve to the specified cell. an iniJal state (Jme t=0) is selected by assigning a state for each cell. a new generaJon is created (advancing t by 1), according to some fixed rule (generally, a mathemaJcal funcJon) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighbourhood. typically, the rule for updaJng the state of cells is the same for each cell and does not change over Jme, and is applied to the whole grid simultaneously, though excepJons are known, such as the stochas8c cellular automaton and asynchronous cellular automaton. The structure of interacJon -­‐ Cellular Automaton The structure of interacJon -­‐ Cellular Automaton ex. Conway Game of Life • 
• 
• 
• 
• 
regular grid of cells. each cell or grid is in one of a finite number of states, such as on and off. the grid can be in any finite number of dimensions. for each cell, a set of cells called its neighbourhood is defined relaJve to the specified cell. an iniJal state (Jme t=0) is selected by assigning a state for each cell. The structure of interacJon -­‐ Cellular Automaton ex. Conway Game of Life Rules: •  Any live cell with fewer than two live neighbours dies, as if caused by under-­‐populaJon. •  Any live cell with two or three live neighbours lives on to the next generaJon. •  Any live cell with more than three live neighbours dies, as if by overcrowding. •  Any dead cell with exactly three live neighbours becomes a live cell, as if by reproducJon. The structure of interacJon -­‐ Cellular Automaton ex. Conway Game of Life Source: Wikipedia The structure of interacJon -­‐ Cellular Automaton ex. Conway Game of Life Source: Wikipedia The structure of interacJon -­‐ Cellular Automaton ex. Conway Game of Life pa]erns and self-­‐organizaJon Source: Wikipedia The structure of interacJon -­‐ Cellular Automaton ex. Conway Game of Life pa]erns and self-­‐organizaJon Classes of emerging pa]ern by Wolfram: •  Homogeneous or Fixed Point -­‐ Class I Stabilize and maintain invariance therea_er •  Heterogeneous or Periodic -­‐ Class II Repeat regularly •  Chao8c -­‐ Class III Irregular and long term unpredictable (but determinisJc) •  Complex -­‐ Class IV Irregular repeJJon The structure of interacJon -­‐ Cellular Automaton DefiniJons of Complexity ‘Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ulJmate, metaphysical sense, but in the important pragmaJc sense that, given the proper8es of the parts and the laws of their interac8on, it is not a trivial ma?er to infer the proper8es of the whole.’ (Simon 1962:468) The structure of interacJon -­‐ Cellular Automaton The key components of Complexity 1.  The system contains a collec8on of many interac8ng objects or agents 2.  These objects’ behavior is affected by memory or feedback mechanisms 3.  The objects can adapt their strategies according to their history 4.  The system is typically open 5.  The system appears to be “alive” The structure of interacJon -­‐ Cellular Automaton The key components of Complexity 6.  The system exhibits emergent phenomena which are generally surprising, and may be extreme. 7.  The emergent phenomena typically arise in the absence of any sort of “invisible hand” or central controller. 8.  The system shows a complicated mix of ordered and disordered behavior The structure of interacJon -­‐ Cellular Automaton Exercise -­‐ The Game of Life • 
Run the Game of Life Model from the NetLogo Models Library • 
Discuss some possible extensions for the model • 
IdenJfy the hypothesis, implement one of these extensions, run the experiments, and discuss the result