Theory Development

EES 4760/5760

Agent-Based & Individual-Based Computational Modeling

Jonathan Gilligan

Class #21: Tuesday, Mar. 27 2018

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Theory Development

Models as a Virtual Laboratory

  • How to use models to run experiments?
  • Strong inference (John Platt)
  • Identify traits (individual behaviors) that give rise to multiple macroscopic patterns
  1. Identify alternative traits (hypotheses)
  2. Implement traits in ABM
  3. Test and compare alternatives:
    • How well did model reproduce observed patterns?
    • Falsify traits that did not reproduce patterns
  4. Repeat cycle as needed. Revise behavior traits, look for additional patterns, etc.

Pattern-Oriented Modeling Cycle

POM Cycle

Example: Trader intelligence

Example: Trader intelligence

Continuous Double Auction

  1. Traders establish buying and selling prices
    • If someone offers a price \(\ge\) selling price, trader sells.
    • If someone offers to sell for \(\le\) buying price, trader buys
  2. Match traders:
    • If traders \(i\) and \(j\) have \(P_{i,\text{sell}} \le P_{j,\text{buy}}\), then transaction occurs.

Zero-intelligence agent

  • Agent sets random buying and selling price
  • If \(P_{i,\text{buy}} > P_{i,\text{sell}}\), then trader \(i\) will lose money.

Minimal-intelligence agent

  • Random buying and selling price with constraint: \(P_{i,\text{buy}} < P_{i,\text{sell}}\).

Results

  • Minimal-intelligence agent was better than zero-intelligence
    • Zero-intelligence produced wild price fluctuations
    • Minimal-intelligence reproduced observed pattern of rapid price convergence
    • Minimal-intelligence also reproduced observed effects of price-ceiling.
  • But simple models had limits:
    • Observed volatility of lower-end prices was not reproduced by models
    • As experimental markets got more complicated, human traders did worse, but models did much worse.

Lessons

Using zero-intelligence as a baseline, the researcher can ask: what is the minimal additional structure or restrictions on agent behavior that are necessary to achieve a certain goal.

Example: Harvesting Common Resource

Example: Harvesting Common Resource

  • Experimental subjects move avatars on screen to harvest tokens
    (like simple video game)
  • Players compete to get most tokens
  • Tokens grow back at some rate
  • Patterns:
    1. Number of tokens on screen over time
    2. Inequality between players
    3. # tokens collected in first four minutes
    4. Number of straight-line moves

Theory development

  1. Näive model: (random) Moves randomly
  2. Näive model: (greedy) Always goes to nearest token
  3. Clever model:
    • Prefers nearby tokens
    • Prefers clusters of tokens
    • Prefers tokens straight ahead
    • Avoids tokens close to other players
  • Näive models do not match any of the four patterns.
  • Ran clever model 100 times for each of 65,536 different combinations of parameters that characterize preferences.

    • Only 37 combinations of parameters matched all four patterns in data.
    • Patterns 2 and 3 are seen for most parameter values
    • Patterns 1 and 4 seen less frequently
    • Therefore:
      • Patterns 2 and 3 are built into the structure of the game.
      • Patterns 1 and 4 may give insight into human behavior.

Example: Woodhoopoe

Example: Woodhoopoe

https://ees4760.jgilligan.org/models/class_21/wood_hoopoe_class_21.nlogo https://ees4760.jgilligan.org/models/class_21/wood_hoopoe_odd.pdf

Observed Behaviors

  • Groups occupy spatial territories
  • One alpha of each sex in a territory
  • Only alpha couple reproduces
  • If alpha dies, oldest subordinate of that sex becomes alpha
  • Scouting forays
    • Subordinate adult leaves territory
    • If it finds territory without alpha, it stays, becomes alpha
    • Otherwise, returns home
    • Risk of predation (death) is high on scouting forays
  • Alpha couple breeds once a year, in December

Observed Patterns

  1. Characteristic group size distribution (adults)

    Group-size histogram

  2. Average age of birds on scouting forays is younger than
    average age of all subordinates.
  3. Scouting forays most common April–October

Modeling Woodhoopoe

  • Start simple:
    • One-dimensional world
    • One tick = one month
    • Every tick, bird has 1% chance of dying (0.99 probability to survive)
    • Scouting forays have 20% chance of death (0.80 probability to survive)
    • Adult subordinates go scouting at random (50% probability each tick)
  • Does model reproduce patterns?

Developing Alternative Strategies

https://ees4760.jgilligan.org/models/class_21/wood_hoopoe_strategies.nlogo