Practical examples of applications of complexity

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Practical examples of applications of complexity

• Financial markets
• Crime
• Unemployment
• Geographical segregation
• Business cycle
• Evolution and extinction of firms
• Adoption of technologies

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Particular problems in social/economic modeling

• Data series are almost always short
• Data series are almost always noisy
• The behaviour of individuals may not be
  time-invariant
• Social/economic modeling is hard

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Modeling complex systems

• Like any science, the key is to make good
  simplifications
• The simplifications relate to the rules of
  behaviour of individuals in the model
• Choose rules of behaviour which can be justified
  independently of the model
• Validate the model by how well it replicates the
  important system-level emergent features

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Some key features of complexity in social and
economic systems

• Individual agents operate with incomplete
  information
• Agents operate under uncertainty
• Agents interact with each other
• The properties of the system as a whole emerge
  from the individual interactions
• Characteristically, the system will lack
  short-term predictability
• But there will be underlying regularities

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Financial markets

• Two key features of price changes
• lack short-term predictability
• high level of volatility
• Conventional economic models have great
  difficulty explaining volatility
• Nobel laureate Kenneth Arrow says this is an
  empirical refutation of the standard economic
  model of competitive equilibrium

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Simple model of financial markets (1)

• A.Kirman Bank of England Quarterly Bulletin,
  1995
•  Has short-term non-predictability
• And high levels of volatility

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Simple model of financial markets (2)

• the model is populated by N agents
• evolves in a series of steps
• at any given point of time, an agent is in one of
  two states of the world ( 0 or 1)
• traders are fundamentalists or chartists (0
  or 1)
• can and do switch between these states

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Simple model of financial markets (3)

• In each step, an agent is drawn at random and
  decides whether or not to change its state of the
  world
• It changes of its own accord with a fixed
  probability ?
• It changes with an additional fixed probability
  ?, which is modified by the proportion of the
  total number of agents which are in the other
  state of the world at that time

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Typical solution of Kirman model
60
55
Percentage of agents who are Chartists
50
45
0
200
400
600
800
1000
Time
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Relative amounts of time for different
percentages of Chartist traders
high propensity to switch behaviour
Relative amounts of time
0
20
40
60
80
100
Percentage of Chartist traders
Figure 1.3
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Schelling model of segregation

• We observe a high level of residential
  segregation on racial lines
• Not just in the US similar issues in the UK
• Does this mean that people are prejudiced?

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Schelling model (1)

• The model contains N agents
• There are equal numbers of two types of agent
• The agents are placed at random on squares on a
  torus
• There is a small percentage of empty squares

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Schelling model (2)

• The 'neighbourhood' of an agent is defined e.g.
  all 8 squares which surround any given square
• An agent is called at random and decides whether
  or not to move
• If an agent moves, it moves at random to an empty
  square

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Schelling model (3)

• The agent moves if more than a specified
  percentage of all agents in its neighbourhood are
  of a different kind to itself
• The model proceeds to the next step, and an agent
  is again called at random to decide whether or
  not to move
• What happens if an agent moves if and only if
  more than 50 per cent of its neighbours are
  different i.e will tolerate a 51/49 split?

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Initial random configuration of agents
50
40
30
20
10
0
0
10
20
30
40
50
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Configuration after only 2 moves per agent
50
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Crime (1)

• In the US (and the UK), massive increases in
  crime in the decades after WW2
• Then falls in last 10 years or so
• Why?

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Crime (2)

• Despite decades of research, no consensus in
  criminology on the impact of incentives on crime
• Impact of prison sentences
• Impact of efficiency of criminal justice system
• Impact of economic circumstances

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Crime model (1)

• N agents
• At any point in time, agent can be in one of 4
  states of the world
• Not susceptible (N)
• Susceptible (S)
• Hard core criminal (C)
• Prison (P)

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Crime model (2)

• Simple rules to describe flows between the states
  of the world
• A key finding in criminology is the importance of
  peer group influence
• The probability of an agent in N moving to S
  depends upon the proportion of agents on its
  social network who are also in S
• The probability of an agent in S moving to C
  depends upon the proportion of agents on its
  social network who are also in C

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Crime model (3)

• This feature frequently generates multiple
  attractors
• In other words, for any given set of economic
  circumstances, sentencing policy etc, there can
  be more than one level of crime

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