# 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

### Continuous Double Auction

• If someone offers a price $$\ge$$ selling price, trader sells.
• If someone offers to sell for $$\le$$ buying price, trader buys
• 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
• 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

## 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
• 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)

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