Session 1: agents, a scenario and a step#

Zoo model: Boltzmann wealth exchange

Goals#

  • Know the three pieces of a Modelly model: a Scenario (the inputs), agents, and a Model with a step.

  • Run a model, read its state, and change a parameter without editing the code.

  • See an emergent result: identical agents trading at random end up unequal.

Before the session: Getting started and the first tutorial, your first model.

Exercises#

1.1 Run KineticWealth with its default scenario and print the richest agent’s wealth and the share of agents with no money at all.

Solution 
from modelly.zoo.kinetic_wealth.model import KineticScenario, KineticWealth

model = KineticWealth(KineticScenario(rng=1))
model.run()
print(model.wealth.max(), (model.wealth == 0).mean())

About a sixth of the agents end with nothing (the stationary law puts probability close to 1 / (money + 1) on zero) and the richest hold several times the mean.

1.2 Every agent starts with money units. Double it. Does the Gini coefficient change? Why?

Solution 
for money in (5, 10):
    model = KineticWealth(KineticScenario(rng=1, money=money))
    model.run()
    print(money, model.datacollector.get_model_vars_dataframe().iloc[-1, 0])

Barely: the stationary law is close to the exponential distribution, whose Gini is 1/2 whatever its mean. With few units per agent the integer law is a little more unequal.

1.3 Read KineticWealth.step in modelly/zoo/kinetic_wealth/model.py. Write, in one sentence each, what the four lines between order = ... and taker = ... do.

Solution

A random permutation of the agents; its two halves are paired element by element; a coin per pair; the coin picks which member of each pair gives and which takes. Every agent trades exactly once per step.

1.4 Change the rule so that a giver passes two units when it has at least two. Copy the model first: modelly zoo copy kinetic_wealth my_wealth.

Solution

In my_wealth/model.py, in step, replace the transfer with:

amount = np.minimum(wealth[giver], 2)
wealth[giver] -= amount
wealth[taker] += amount

wealth[taker] += amount is safe because every agent appears once in the matching, so no index repeats.