The Basics of agent-based modeling

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# The Basics of agent-based modeling
### David Garcia, Petar Jerčić, Jana Lasser TU Graz
### Computational Modelling of Social Systems

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<div class="my-footer">David Garcia - Computational Modelling of Social Systems</div>

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# About me

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Website: [dgarcia.eu](https://dgarcia.eu)

Twitter: [@dgarcia_eu](https://twitter.com/dgarcia_eu)

Github: [dgarcia-eu](https://github.com/dgarcia-eu)

Email: dgarcia@tugraz.at
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- Professor for Computational Behavioral and Social Sciences at TU Graz
- Faculty member of the Complexity Science Hub Vienna
- Group leader at the Medical University of Vienna

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# Overview

## 1. Complex Social Behavior

## 2. Agent-Based Modelling (ABM)

## 3. ABM Example: Date Choice Model

## 4. About this Course

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# Complex Social Behavior

## *1. Complex Social Behavior*

## 2. Agent-Based Modelling (ABM)

## 3. ABM Example: Date Choice Model

## 4. About this Course

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## Complex social behavior example: Polarization
<img src="Figures/Polarization.jpg" width="650" style="display: block; margin: auto;" />

- Two opposing groups can become more extreme due to their perception of the behavior and opinions of the other group. 
- Individuals in isolation do not naturally tend to opinion extremes.
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## Complex social beavior example: Bank runs
<img src="Figures/BankRun.jpg" width="600" style="display: block; margin: auto;" />
- Banks operate without all the savings in their reserves
- If customers believe that many others withdraw their money, they will do it too
- The rumor and spreading distrust is necessary, customers in isolation would not create a bank run (tragedy of the commons)
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## Complex social beaviors: Activation and inhibition

- Individuals demonstrating in isolation are peaceful, but in a group a riot can emerge without a clear antecedent
- People alone in the street offer help, but when many are watching they don't act (bystander effect)

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# The macro-micro gap

*Causal Mechanisms in the Social Sciences. Peter Hedström and Petri Ylikoski. Annual Review of Sociology, 2010.*
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## Interdisciplinarity in complex social behavior
<img src="Figures/Interdisciplinarity.svg" width="1200" style="display: block; margin: auto;" />

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# Agent-Based Modelling (ABM)

## 1. Complex Social Behavior

## *2. Agent-Based Modelling (ABM)*

## 3. ABM Example: Date Choice Model

## 4. About this Course

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# Agent-Based Modelling (ABM)

- Agent-Based Model: A computational analogy of a social system that is composed of a set of agents that represent *discrete* individuals

- Agents have internal states, perceive the actions of other agents, and interact with other agents and their environment (*situated*)

- Agents are *active*: they have a behavioral repertoire, are not just particles

- Agents might have access only to *limited informtion* in their environment

- Agents might have *internal goals* that determine their behavior and can *adapt* to the behavior of other agents or the environment

*Agent-Based Modeling: A New Approach for Theory Building in Social Psychology. Eliot Smith and Frederica Conrey, 2007*

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# Explaining behavior with ABM

- Observed collective behavior or effects are *explananda*: empirical facts that are missing an explanation.
  - Example: hotter days have higher average crime rates

- ABM offer *explanations*: theories that generate the observed behavior and link it to other empirical facts
  - Example: heat makes people be longer in the street, facilitating crime

- ABM are part of a larger theoretical approach called *Analytical Sociology*, where everything in a model of social behavior must be explicit
  - Example: coding a simulation of people going out depending on temperature and crimes happening outdoors
  
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# Explaining behavior with ABM

**ABM do not provide empirical evidence**
  - Simulation results alone are not evidence that humans behave in one way or another. Beware of causal conclusions based on ABM alone!

- They can **generate hypotheses**, for example on the consequences of policies in simulations or formulate predictions

- They can **reconcile empirical observations** across individual behavior and collective behavior levels

- They are a way to **analyze theory**, showing necessary or sufficient conditions for some collective behavior to emerge
  
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## Computational theory instead of exploration

**ABM are for analysis, not just exploration**

- Exploring what happens in a simulation is fine, but ABM can do much more!

- **Behavior calibration** of individual agents with experiments or surveys: integrating social and behavioral findings in an ABM

- **Analysis of observable outcomes** versus parameters of behavior or alternative mechanisms/policies

- **Testing outcomes** with large-scale data (e.g. digital traces from computational social systems), across conditions and over time

*From factors to actors: Computational Sociology and Agent-Based Modeling. Michael Macy and Robert Willer. Annual Review of Sociology, 2002.*

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# Properties of good ABM

- They **model causation**: agent actions and conditions have counterfactuals and dynamics are not ad hoc to get an outcome

- They have **measureable outcomes:** collective behavior can be aggregated into one or more quantities that can be measured in many simulations and across conditions

- They have **quantifiable designs:** individual dynamics are based on metrics that can be tested with empirical methods (e.g. experiments, surveys)

- Are **minimal and modular:** you can test the sensitivity of outcomes with different blocks of dynamics and include only what is necessary

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# ABM Example: Date Choice Model

## 1. Complex Social Behavior

## 2. Agent-Based Modelling (ABM)

## *3. ABM Example: Date Choice Model*

## 4. About this Course
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## Date choice in computational social systems

.pull-left[![](Figures/Tinder1.png)]

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## Date choice in computational social systems

.pull-left[![](Figures/Tinder1.png)]

.pull-right[![](Figures/tinder-tender.gif)]
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# The question of attractiveness matching

- Example: Kalick and Hamilton (1986) date choice model

-   Question: do people seek dating mates that are as attractive as possible or matching their own perceived attractiveness?
  
- Conflicting evidence: 
  - In experiments (micro), participants seek to maximize partner attractiveness, participant attractiveness is barely relevant
  - In observational data (macro), attractiveness of couples are   correlated  
  ( `\(r \sim 0.6\)` ) and correlation is stronger for more committed couples

*The matching hypothesis reexamined. Michael Kalick and Thomas Hamilton. Journal of Personality and Social Psychology, 1986.*
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# The Kalick and Hamilton dating model

- Start with N male and N female agents, all are uncoupled

- Each agent has a constant attractiveness number randomly sampled between 1 and 10 at the beginning of the simulation

- Repeat while there are uncoupled agents:

- All male and female agents are randomly paired for a date

- Dates consist on each individual accepting or rejecting their     partner. Probability of accept is based on a rule taking into account their attractiveness levels (e.g. matching or seeking attractiveness)

- Dates with both agents accepting form a couple and leave the dating pool

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# Model metrics

1. Model "time" `\(t\)`: Percentage of agents that are in a couple
  - It grows with simulation iterations, starting from `\(0\)` and approaching `\(100\)`
  
2. Correlation coefficient between paired couples ( `\(r_t\)` ) at time `\(t\)`:
  - `\(r_t = r(M_t, F_t) = \frac{\sum_{c \in C_t}(m_c - \mu_{M_t})(f_c - \mu_{F_t})}{\sqrt{\sum_{c \in C_t}(m_c - \mu_{M_t})^2(f_c - \mu_{F_t})^2}}\)`
  - `\(M_t\)` and `\(F_t\)` are the vectors of male and female attractiveness in couples formed up to time `\(t\)`, denoted as `\(C_t\)`

3. Mean attractiveness of the `\(N_t\)` paired couples at time `\(t\)`: 
  - `\(\mu_t = \mu_{M_t} + \mu_{F_t} = \sum_{c \in C_t}  (m_c+f_c) / N_t\)`

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# Seeking similar match: outcomes

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- Outcomes over simulation time (% matched couples) for the case of seeking similar partners

- Correlation starts very high (0.8)

- No real trend in correlation

- Mean couple attractiveness is around the average the whole simulation

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# Maximizing partner attractiveness

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<img src="Figures/preference.png" width="550" style="display: block; margin: auto;" />
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- Outcomes over simulation time (% matched couples) for the case of preferring attractive partners regardless of own attractiveness

- Correlation starts low but raises pretty fast up to about 0.55

- Mean couple attractiveness starts much above average and approaches average

- Attractive agents couple earlier
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# Results of dating model

- **Main result:** attractiveness matching is not necessary for observed correlations, they can be produced by attractiveness seeking alone.

- ABM reconciles apparently conflicting empirical results

- **Comparison with empirical data:** observed empirical correlation is closer to 0.55 than to 0.9
  - This could also be due to measurement error in attractiveness 
  
- **Many simplifications**

*The matching hypothesis reexamined. Michael Kalick and Thomas Hamilton. Journal of Personality and Social Psychology, 1986.*

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# About this Course

## 1. Complex Social Behavior

## 2. Agent-Based Modelling (ABM)

## 3. ABM Example: Date Choice Model

## *4. About this Course*
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# Course objectives

1. Understanding how to **formulate and analyze** computational models of social systems.

2. **Integrating knowledge** about social dynamics and analytic tools to understand the **complex behavior** of social systems.

3. Acquiring programming skills to **implement, simulate, and visualize** computational models of social systems

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# Course topics

### Block 1: Fundamentals of agent-based modelling

1- **Basics of agent-based modelling: the micro-macro gap**  (03.03.2022)  
*Tutorial: ABM basics in Python with Mesa (session 1)*

*(Please install Jupyter and iPython as soon a possible)*

2- **Modelling segregation: Schelling's model**  (10.03.2022)  
*Tutorial: ABM basics in Python with Mesa (session 2)*

3- **Modelling cultures**  (17.03.2022)  
*Exercise 1: Schelling's model and Pandas (session 1)*

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# Block 2: Opinion dynamics

4- **Basics of spreading: Granovetter's threshold model**  (24.03.2022)  
*Exercise 1: Schelling's model and Pandas (session 2)*

5- **Opinion dynamics**  (31.03.2022)  
*Exercise 2: Threshold models (session 1)*

6- **Modelling hyperpolarization and cognitive balance**  (07.04.2022)  
Guest lecture by Simon Schweighofer (Online)    
*Exercise 2: Threshold models (session 2)*

*No class between 9.04.2022 and 23.04.2022: Easter holidays*

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# Block 3: Network formation

7- **Basic network models**  (28.04.2022)  
*Exercise 3: Bounded confidence (session 1)*

8- **Modelling small worlds**  (05.05.2022)  
*Exercise 3: Bounded confidence (session 2)*

9- **Scale-free networks**  (12.05.2022)  
*Exercise 4: Scale-free networks and visualization (session 1)*

10- **Growth processes**  (19.05.2022)  
*Exercise 4: Scale-free networks and visualization (session 2)*

*No class on 26.05.2022: Ascension day*

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# Block 4: Behavior on networks

11- **Modelling spreading in networks**  (02.06.2022)   
*Project guidance*

12- **Modelling epidemics: the SEIRX model** (09.06.2022)  
*Project guidance*

*No class on 16.06.2022: Corpus Christi*

13- **Project presentations**  (23.06.2022)

14- **Project presentations**  (30.06.2022)

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# Time, place, online

- Lecture time:  Thursdays at 16:15 (sharp)
  - Lecture place: HS F today, from next week in HS i7
- Exercise group 1 time: Thursdays after Lecture (approx. 18:00)
  - Exercise group 1 place: Same room 
- Online exercise support group 2: Wednesdays at 13:00 (sharp)
  - Online in Webex

Handouts, codes, and data can be found on the Github repository of the course: https://github.com/dgarcia-eu/ComputationalModellingSocialSytems

**1-2 readings for each lecture:** Links on github and PDF on Teach Center

Computational Modelling of Social Systems Discord (only this course): https://discord.com/invite/VSE9r9GtR8 Use it to ask for help!

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# Course assessment

Exercises done in groups of **one or two** students
- Exercise 1: ungraded
- Exercise 2: 25% of final grade. Deadline: 20.04.2022
- Exercise 3: 25% of final grade. Deadline: 18.05.2022
- Exercise 4: ungraded

Final group project in groups of **up to four students**:
- Participation in group presentation sessions: 25% of final grade
  - All group members **must participate** in their presentation
  - Each group is assigned as a **discussant** for another group
  - **Attending both presentation sessions is mandatory**
- Project report and codes: 25% of final grade
- More details on project topics and reporting will follow later in the course

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# Summary

1. **Complex Social Behavior**
  - Humans behave differently in groups as in isolation: collective behavior
  - Interdisciplinary approach to explain macro dynamics from micro behavior
2. **Agent-Based Modelling (ABM)**
  - A computational approach to formalize and analyze social systems
  - Agent properties and model objectives and assumptions
3. **ABM Example: Date Choice Model**
  - Mismatch in empirical results: observations contradict experiments
  - A simple model shows that seeking attractiveness in a finite dating pool also generates the observed correlations in couples
4. **About this Course**
  - ABM basics, opinion dynamics, network models, behavior on networks
  - Readings-base
  - Following: Introduction to Mesa for ABM