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Showing Revision 5 created 04/16/2018 by ComplexityExplorer.

  1. Today we're going to explore the
    relationship of agent based modelling
  2. to other methods that you might use to
    explore complex systems.
  3. I'm going to start by talking about ABM
    versus equation-based modelling (EBM),
  4. which is a phrase that's been around for
    a while
  5. to describe a set of techniques such as
    analytical or game-theoretic modelling
  6. in which you write first principle
  7. and then you see where those might take
  8. These are often compared because agent
    based modelling in many ways
  9. starts a lot with some of the same first
  10. but then goes in a different direction,
  11. rather than looking for a closed form
  12. it tries to come up with computational
    solutions to the problem at hand.
  13. So why might you use agent based modelling
    instead of equation based modelling?
  14. Many equation based models make the
    assumption of homogeneity -
  15. in fact they have to in order to generate
    the closed form solutions
  16. that they're famous for.
  17. So in many cases you have a system that's
    dramatically affected by heterogeneity
  18. and so using something like agent based
  19. when it's not possible to generate a
    closed form solution
  20. for a heterogeneous system, might be a
    good way to approach the problem.
  21. Also, a lot of equation based models are
    continuous and not discrete.
  22. This leads to something called the nano-
    wolf problem
  23. The idea is that if you are modelling
  24. that is essentially a discrete entity,
    like a wolf for instance,
  25. then if I have an equation based model
    that allows the wolf population
  26. to drop to one-tenth of a wolf, or one
    millionth of a wolf,
  27. theoretically, under a lot of equation
    based models, it could still rebound
  28. and come back from that low level.
  29. In reality, once the last wolf,
  30. or more importantly, the last mating pair
    of wolves die
  31. there's no way for the population to
    rebound at that point.
  32. Which means that using a discrete solution
    often provides you with a better answer.
  33. Now it's not the case that all equation
    based models are continuous
  34. but it's just one of the reasons why ABM
    provides you with a more natural ontology
  35. to that space.
  36. Many equation based models are written at
    the aggregate level
  37. rather than the individual level
  38. which requires you have knowledge of the
    overall patterns of behaviour of the system
  39. rather than the individual entities
    within the system.
  40. It's often easier to get individual level
  41. rather than aggregate descriptions
  42. and so as a result ABM often works better
    in those contexts.
  43. Related is the fact that the ontology of
    an EBM is often at that same global level
  44. whereas the ontology of an ABM is at the
    individual level
  45. making it easier to communicate the ABM
    to someone else
  46. since you're describing individual
  47. Also, most EBMs will not provide you with
  48. about what a particular individual does
    within the model.
  49. ABMs allow you that drill-down detail,
  50. which means in many cases you can go back
    and figure out
  51. exactly how important an individual is to
    the complex system.
  52. You can relate all those notions to the
    fact that EBMs are kind of 'top down' -
  53. starting with these big entities and then
    modelling down lower and lower systems
  54. whereas ABMs start with the premise of
    understanding the local system
  55. and then model upwards.
  56. That being said, EBM does have several
    advantages over ABM.
  57. One of them is that they're usually more
  58. for the set of assumptions that are
    assumed about the model.
  59. On the other hand, those assumptions are
    usually restrictive
  60. for all the reasons we've previously
  61. and so therefore it's difficult to use
    them in a lot of real-world situations.
  62. In fact, we would argue that ABM should be
    viewed as a complement to EBM,
  63. in fact you can build ABMs that are essentially
    instantiations of game-theoretic models
  64. and then explore the ramifications beyond
    the closed-form solutions
  65. that are very often obtained using EBMs.
  66. Of course, EBM is not the only approach,
  67. you can also do statistical modelling
    which in many ways also uses equations
  68. but it's done in a different way.
  69. Here, the idea is that we take aggregate
    patterns of behaviour about the world
  70. and then infer a model relating the entities
    of those aggregate patterns together
  71. so you do a regression or something like
  72. And many times when you have a statistical
  73. it's very hard to link it to first
    principles or behavioural theory
  74. that describe the way the agents take
    action in that system.
  75. And you need to have the right data to do
    statistical modelling.
  76. ABM can complement statistical modelling
  77. by building from first principles to
    generate statistical data
  78. which you can then compare with
    statistical data obtained from the real world.
  79. Another approach you might want to use is
    to conduct a series of lab experiments
  80. such as behavioural economics experiments.
  81. Lab experiments are often very useful
    because they can actually generate theory,
  82. you can set up a condition and then really
    see whether a particular theory
  83. seems to hold up within that space.
  84. However lab experiments are often not as
    powerful as they could be
  85. because they're rarely scaled up to large
    conditions like we see in the real world.
  86. Instead, you're looking at maybe six or
    seven individuals and how they interact,
  87. or how they make decisions.
  88. Agent based models can be created from
    lab experiments
  89. you essentially can use the rules that
    you've inferred from the lab experiments
  90. to construct your agent based model.
  91. As a result you can explore what would
    happen if everyone acted
  92. the way my lab experiment says people
  93. And then you can use that to generate new
  94. about things you might see in the world
    that you don't actually see in the lab,
  95. construct a new lab experiment,
  96. and see if you can uncover any evidence
    for those new hypotheses.
  97. You can also try to manipulate parameters
    of the model
  98. beyond what the lab experiments will
  99. A lot of times you can't impose, say, a
    hundred different conditions
  100. on a lab individual, because of the fact
    that they won't stand for that many tasks.
  101. Agent based models don't care how many
    conditions you impose on them.
  102. So if you can create the behavioural
    pattern of a lab experiment
  103. you can then run it through as many
    different instantiations as you need to.
  104. Agent based modelling can compare
    generative principles drawn from lab experiments,
  105. so say we have two lab experiments that
    provide you with different evidence
  106. about the way the world works.
  107. You can generate an agent based model
    from each of them
  108. and see which one matches up better with
    the real world.
  109. Finally, there are a lot of aggregate
    computer modelling
    and simulation approaches
  110. that you might use instead of agent
    based modelling.
  111. For instance, system dynamics modelling
    is an approach which embraces
  112. a system level approach to the entire
  113. using stocks and flows to talk about the way
    different parts of the world affect each other.
  114. The problem is that most of these
    approaches lack the individual level representation
  115. and in fact one of the best things you can
    possibly do
  116. would be maybe combine some of these
    system level approaches
  117. with the individual level approach of
    agent based modelling.