2.2.3: Time

import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
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2.2.3: Time#

Every agent-based model advances through time, but how it does so is a design choice with real consequences. This section looks at how an ABM chops continuous time into discrete steps (called ticks), what happens inside a single step, and why the order in which agents take their turn can change the outcome of the whole model.

2.2.3.1: Discrete and continuous time#

Time can be represented as continuous or discrete, and the choice determines when the model permits state to change. In continuous time, an event may occur at any real-valued moment; in discrete time, the model groups change into separate intervals. A finer interval can represent faster processes and reduce discretisation artefacts, but it also requires more updates and may imply a precision the available evidence does not support. The time representation should therefore follow both the process being studied and the temporal resolution of the data used to describe it.

Continuous Time: Time flows smoothly, and events or state changes can occur at any precise, real-valued moment.

Discrete Time: Time is broken into distinct, separate intervals, jumping directly from one point to the next.

2.2.3.1.1: Tracking time in ABM#

While reality may be continuous, ABM inherently operates in discrete time. Because a simulation processes its instructions sequentially, time must be discretised into fixed units called ticks. In an ABM, all agent actions and environmental updates are calculated within a single tick before the model advances to the next. Because the computer executes these calculations one agent at a time, the order of agent iteration is critical to simulating real-world parallelism accurately, without introducing processing bias [1]. We return to exactly this point in Section 2.2.3.4, where a simple five-farmer example shows how changing only the order in which agents act changes who ends up with what.

Time can advance in fixed ticks or flow on continuously; the short activity below asks you to tell the two apart.

Learning Activity: Discrete or continuous time?
tell fixed-tick systems apart from ones whose events fall at any instant.
Six systems, from a turn-based board game to randomly decaying atoms, each to be judged as advancing in fixed discrete steps or in continuous time whose events fall at arbitrary real moments.
For each system choose Discrete (everything updates each tick) or Continuous (events happen at arbitrary real moments), then press Check.

Whether a model advances in discrete ticks or in continuous, event-driven time is itself a modelling choice, and it should follow the system being represented.

2.2.3.2: Inside a time step#

The following example shows what happens within a single time step, using a wealth-redistribution model in which agents randomly take money from each other:

Time Step Flow in a Money Model

Fig. 20 Figure 2.6 Time Step Flow in a Money Model.#

This diagram illustrates the sequence of actions that occur within a single discrete time step in an agent-based money redistribution model. Each agent follows the same process: (1) randomly selects another agent, (2) decides how much money to attempt to take, (3) checks if the target agent has sufficient funds, and (4) executes the transfer based on availability. This demonstrates how individual agent decisions accumulate into system-level wealth dynamics over multiple time steps.

This flowchart shows the key phases within a single time step:

Learning Activity: Inside a single time step
trace the five phases an agent follows during one model time step.
A wealth-redistribution model in which every agent repeatedly senses its surroundings, chooses a target and action, attempts a transfer, updates the agents' balances, and then advances to the next step.
Select a numbered phase, or use Previous and Next, to connect each general phase with its concrete role in the money model.

2.2.3.3: Interactive time stepping#

A time step is easier to understand when the transition can be inspected rather than played as a continuous animation. In the Boids simulation below, each click of “Next Step” advances the model by exactly one tick. Compare the state before and after the click: every bird senses nearby birds, adjusts its direction according to the same local rules, and moves to a new position. No rule specifies the flock’s overall shape, yet repeated local updates make that shape change over time.

Stepping manually is also a verification technique. It lets you check whether agents respond to the information they should have at that moment, whether an update is applied once per tick, and whether an unexpected collective pattern can be traced back to a particular transition. Once those individual transitions make sense, continuous playback simply repeats the same model step faster.

Animated model output

2.2.3.4: Activation order#

A tick defines the interval over which the model advances, but it does not by itself define how the agents share that interval. The activation scheme decides whether agents act from a common state, observe changes made earlier in the same tick, or move through separate decision and update phases. Because that choice can alter both individual opportunities and system-level outcomes, it belongs in the formal model and should be reported with the results.

2.2.3.4.1: Time and activation order#

Inside one time step, a computer still executes instructions in some order. Under sequential activation, an early agent can change the state that later agents observe; under simultaneous or staged activation, agents decide from the same snapshot and changes are committed together. A fixed order may therefore create a systematic first-mover advantage, while random shuffling distributes that advantage across runs but can still produce path-dependent histories. Activation is not merely a programming detail: it is an assumption about information, timing, and whose action can affect whom within the same step.

Learning Activity: Does activation order matter?
compare how random, fixed, and simultaneous activation change a model's behaviour.
Three scheduling strategies for deciding the order in which agents act during one time step, each with different implications for bias, realism, and within-step influence.
Open each schedule card and compare its defining rule, its advantages, and the artefacts it may introduce.

The first activity isolates the logic: decide which rules are sensitive to ordering and which are not. The next one turns that abstract choice into a distributive consequence by asking who obtains a scarce resource when farmers act in different sequences.

Learning Activity: Who gets the water?
see how activation order alone decides who thrives and who runs dry.
Five farmers share a well that refills to 10 units each round, while every farmer wants up to 3 units; one panel always activates A through E in order and the other reshuffles them every round.
Press Run to compare the schedules over many rounds, use Step to inspect one round, and watch the gap between the farmer who collected the most and the one who collected the least.
Fixed order (A, B, C, D, E)
0A
0B
0C
0D
0E
gap, most minus least: 0 units
Random order each round
0A
0B
0C
0D
0E
gap, most minus least: 0 units
round 0  ·  bars show each farmer's total water collected
The takeaway: With a fixed order, the same farmers always draw first and take their fill while the last ones repeatedly find the well empty, so lasting inequality builds up. With a random order, the chance to go first rotates and the shares become fairer over many rounds. Every farmer follows the same rule; only the activation order differs.

Choose an activation scheme that matches the process being represented, document it, and test whether the conclusions survive a plausible alternative order.

Key takeaways#

Key takeaways

  • Simulation time may advance in fixed ticks or through events, and that choice must match the system being represented.

  • Within a tick, agents perceive, decide, act, and update shared state before the model advances.

  • Activation order is part of the model: a fixed order can create persistent advantage, while reshuffling distributes who acts first.

  • Interactive stepping is useful for verification because it makes one transition inspectable at a time.

Time settles when agents act and in what order. The remaining question is what happens when they do act on one another, that is, how agents interact. That is the subject of the next section, 2.2.4 Interactions.

References#