Agent-based simulation

Overview

An agent-based simulation keeps one record per individual (a person, a household, a firm, an institution) and advances all of them in discrete steps. Each step, every agent runs its rules, and the outcome that matters, such as an infection peak or a change in wealth, is read off the population as a whole. The paper that motivates its approach argues that equation-based SIR and SEIR models cannot represent individual movement, household and workplace structure, or economic exchange at the level it wanted 2006.10532 §1 2006.10532 §2.

The shared invariant across variants is the step loop: agents act, then pairwise contacts are checked, then summary statistics are recorded 2006.10532 alg. 1. What differs between variants is which agents exist, how they move, what a contact means, and whether money or other resources flow between them.

This page rests on five variant cards and one position paper, and they differ in kind. The first is a classic agent-based model with a step loop and contacts. The second uses a language model as the behaviour of each agent, but runs its participants one at a time and has no contact step. It is included because its participants are simulated individuals, not because it shares the loop. The third uses language-model agents that influence each other over a fixed communication graph, in rounds, which brings the interaction step back. The fourth uses language-model agents that share a scarce economy and act one at a time each day, so robbery and trade are resolved between agents. Its day loop is turn-based and has no distance check. The fifth uses language-model agents in fixed roles that pass one paper through a staged review. It has no step loop, and its agents meet only once, in one discussion phase. The position paper proposes no variant; it is cited for the validation step it asks for. Other agent-based designs are not covered until more cards exist.

Variants

Hourly agent-based SEIR with economic coupling

The COVID-ABS model runs one iteration per hour for two months of simulated time 2006.10532 §4. Its agent types are a person, a house (a group of people who share bills), a business, a government and a health system. The person agents move on a fixed daily routine of rest, work, lunch and recreation 2006.10532 tab. 4 2006.10532 eq. 5–8. Infection spreads when two person agents are within a contact distance, with a fixed probability per contact 2006.10532 §3.3.2. Business contacts move money from people to businesses, and a monthly accounting step moves taxes, wages and funding between agents 2006.10532 §3.3.3. Its scenarios are compared on deaths, infection peak and per-group wealth change, each averaged over 35 runs 2006.10532 §4. Card: COVID-ABS.

Use this variant as a template only for its structure. Its numbers come from Brazilian data and the authors' own choices, and several are marked by the card as not stated or internally inconsistent (see Contradictions).

LLM-simulated participants (Turing Experiments)

A Turing Experiment is a program that writes zero-shot prompts for a named participant, queries a language model and records the completion, then repeats this over many participants 2208.10264 §1 2208.10264 §2. Each participant is a separate run. The method as described has no step loop that advances shared state and no contact check between participants, so the agent-to-agent interaction that defines the classic variant is absent. Four experiments are simulated: the Ultimatum Game, garden-path sentences, the Milgram shock study and a wisdom-of-crowds estimation task 2208.10264 §4 2208.10264 §5 2208.10264 §6 2208.10264 §7. The Milgram experiment is the one multi-step loop, and it runs one subject's record forward with judges at each stage, not a population of interacting agents 2208.10264 app. F.1.

Reported results are author-reported and come from OpenAI text models. The simulated Ultimatum Game shows a gender difference in acceptance of a $2 offer, 60% for a man receiving from a woman and 20% for a woman receiving from a man 2208.10264 §4 2208.10264 fig. 5. In the Milgram study, the simulated subjects show 75 of 100 obedient to the end, against 26 of 40 in the human reference 2208.10264 fig. 7. In the wisdom-of-crowds task, the newer models give a normalized median of 1.0 with zero spread on every question, where the human answers are spread out 2208.10264 fig. 8 2208.10264 tab. 3. The authors read this as a distortion from hyper-accuracy, and they suspect alignment training without testing the cause 2208.10264 app. E. Card: Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies.

LLM agents on a communication graph (Physics of Agents)

A community of 32 language-model agents, each with a fixed persona, runs synchronous rounds over a signed communication graph 2608.16578 §2. In each round every agent writes one message from its current opinion and inbox. Messages are routed along friendly (+1) and unfriendly (−1) ties, and each agent then casts five binary votes whose mean sets its state 2608.16578 §2. The paper runs eight rounds 2608.16578 §2 fn.. The shape matches the classic step loop, with graph edges in place of a distance check: agents act, interact along edges, and the state is recorded.

The paper's main claim concerns the group, not one agent. A logistic update with three couplings (concordant, discordant and unsigned ties, plus a persona-and-question field) is fitted to observed one-step votes. It predicts each agent's next vote and how often each group outcome occurs 2608.16578 §4 2608.16578 §5.2. Groups are sorted into indifference, polarization and consensus by conviction 2608.16578 §3.2. On the held-out tests the three-coupling rule reaches 75.1% to 86.3% one-step balanced accuracy across four models, both question types and in- and out-of-distribution graphs, and the authors report it best in 15 of 16 graph columns 2608.16578 tab. 1 2608.16578 tab. 2 2608.16578 §5.1. Rollouts that feed predictions back score lower 2608.16578 tab. 1. The fitted couplings say the concordant weight is larger than the discordant one in every model 2608.16578 tab. 3 2608.16578 §5.4. Card: Physics of Agents.

The agents are simulated personas, not people, and the test set is small (20 objective and 10 subjective questions) 2608.16578 app. Tasks. The authors caution against reading the fit as a model of human opinion 2608.16578 §7.

Validity is the gate for every result. The valid share of completions ranges from 51.0% for text-ada-001 on the wisdom-of-crowds prompts to 99.5% for text-davinci-002 on the Ultimatum Game 2208.10264 tab. 1. The authors say to tune prompts until validity is "sufficiently close to 1" before any hypothesis test, but give no threshold 2208.10264 §2. The authors also say these models were probably trained on descriptions of the studies, which is why they added novel variants 2208.10264 §3 2208.10264 app. F.2.

LLM agents in a scarce shared economy (Artificial Leviathan)

Nine language-model agents share two assets, food and land. Each starts with 2 food and 10 land and uses one food a day 2406.14373 §3.1 2406.14373 §4. Each agent has three traits drawn at random at the start: aggressiveness, covetousness and strength 2406.14373 §3.2. It also keeps a text memory of its last 30 actions 2406.14373 §3.2.

Each day every agent first answers any action aimed at it, then takes one action of its own: farm, rob, trade or donate 2406.14373 §4 2406.14373 §3.3. A robbery target either resists, in a contest whose win chance is a sigmoid of the strength gap 2406.14373 eq. 1, or concedes. Conceding makes the robber a permanent superior, and the target's subordinates submit to the robber as well 2406.14373 §3.3 2406.14373 app. D. The amounts moved are chosen by the language model 2406.14373 §4 2406.14373 app. B.

The authors read the runs as a move from open conflict to a single sovereign, and compare the path with Hobbes's account of a social contract 2406.14373 §1. Averaged over 85 runs, the robbery rate falls from 0.391 before a sovereign forms to 0.037 after, and the farm rate rises from 0.477 to 0.737 2406.14373 §7.2 2406.14373 fig. 6. Donation is available in the prompt, and no agent ever chose it 2406.14373 §8.6. Card: Artificial Leviathan.

The paper's results are for one proprietary model and a single world, and the authors give no external baseline 2406.14373 §5. Several design details are not stated: the outcome of a contest, the stop rule, the model snapshot, temperature and output limit 2406.14373 §3.3 2406.14373 §4 2406.14373 §7 2406.14373 §9. The paper also reports its "±" values without saying whether they are standard deviations or standard errors 2406.14373 §7.2.

LLM reviewers in a staged simulated conference (AgentReview)

AgentReview fills the roles of an ICLR-style review with language-model agents: three reviewers, an author who answers each review, and an area chair (AC) who leads the discussion, writes a meta-review and makes the decision 2406.12708 §2.1. Each role has a written profile. Reviewers are given a commitment, an intention and a level of knowledge, and the AC is given one of three styles 2406.12708 §2.1. A paper goes through five phases: reviews, rebuttals, a reviewer–AC discussion, a meta-review and a batch decision 2406.12708 §2.2 fig. 2. Reviewers see only the paper and their own review until the discussion, which is the one phase where they meet 2406.12708 §2.2.

The design is a baseline comparison. A run with no trait prompts is the reference, and each setting changes one trait, for example by replacing one reviewer with a malicious one 2406.12708 §2.4. Over the 523 ICLR 2020–2023 papers, a malicious reviewer lowers the average rating from 5.110 in the baseline to 4.368 after discussion 2406.12708 tab. 1. Its final decisions agree with the baseline on 62.91% of papers, against 86.62% for a benign reviewer 2406.12708 tab. 2. The paper calls its results statistically significant, but reports no significance test and no repeated runs 2406.12708 §1. A human comparison on 100 papers matches at least two, three and four of four major comments in 90%, 77% and 39% of papers 2406.12708 app. A.4. Card: AgentReview: Exploring Peer Review Dynamics with LLM Agents.

The authors advise against using LLM reviewers in real peer review, and the simulation is never compared with real review outcomes [arxiv:2406.12708 Limitations]. The card supports comparisons between the paper's own settings, not claims about how real reviewers behave.

When to use which

Implementation sketch

A discrete-time loop over agents, with a pairwise contact check each step. The core is shared by the classic variant above. Its per-type actions, the contact rules and the bookkeeping differ, as the card describes 2006.10532 alg. 1.

# Discrete-time agent loop with pairwise contacts  [arxiv:2006.10532 alg. 1]
# Input:  P (parameters), T (number of steps)
# Output: one summary per step

def run_simulation(P, T):
    # Create agents and place them in the space  [arxiv:2006.10532 §3.2]
    agents = initialize(P)
    summaries = []
    for t in range(1, T + 1):
        # Each agent runs its rules for this step  [arxiv:2006.10532 §3.3]
        for agent in agents:
            agent.execute_actions(t, P, agents)
            if agent.is_person:
                # Pairs within the contact distance interact  [alg. 1]
                for other in agents:
                    if other is not agent and dist(agent, other) <= P.delta:
                        agent.contact(other)
        # Record the summary statistics for this step  [arxiv:2006.10532 tab. 3]
        summaries.append(summarize(agents))
    return summaries

Notes for implementers:

• The card does not give a value for the contact distance δ. Table 2 gives a contact distance of 1 unit, and the card notes that whether δ equals it is not stated 2006.10532 tab. 2 2006.10532 §3.3.
• The contact check as written is O(n²) per step. A spatial index would change the cost, but the card does not describe one, so any such choice is ours to make.
• Dead agents are moved to a fixed position. Whether they still count in summaries is not stated 2006.10532 §3.3.1.
• The Turing Experiment variant does not use this loop. Its unit is one participant's prompt and completion, repeated over names and conditions 2208.10264 §2. Its per-run cost depends on the number of queries and the record length, not on a contact check.
• The AgentReview variant also has no step loop. It runs fixed phases over one paper, then a batch decision. Its comparisons use a trait-free baseline, and when one reviewer changes the paper reuses the baseline's first two phases 2406.12708 app. A.2. Regenerate the baseline before comparing settings. The paper ran gpt-4-1106-preview 2406.12708 app. A.2, but the released code defaults to a different model (see that card's Paper vs code notes), so pin the model yourself. The paper does not state temperature or output-length limits, so those are choices to record.
• The graph variant keeps the round shape, with edges in place of the distance check. Each round costs one message and K votes per agent, so N + N·K model calls, with K = 5 in the main runs 2608.16578 §2. The paper does not state the number of edges, so an implementation has to choose one 2608.16578 app. Communication Networks.
• The shared-economy variant also runs in turns, not in a step loop with a distance check. Each robbery is resolved by a reply from the target before the next action 2406.14373 §4. The paper does not give the turn order or the stop rule, so an implementation has to choose both. Each decision is one model call, so calls grow with agents and days, and the paper gives no count per day 2406.14373 §4.
• The coupling split is not unique. Only some combinations of the three couplings are identified, and the reported values depend on fitting order 2608.16578 tab. 3 2608.16578 app. Fitting. Do not compare β+ or β- across papers without that caveat.

Contradictions

Two open tensions, each side cited:

• The Turing Experiment paper reports that the recent models reproduce the human trend in three of four studies 2208.10264 §4 2208.10264 §5 2208.10264 §6. The position paper argues that matching a trend on a niche task is not enough to trust a simulation 2501.08579 §6. It cites other studies where an LLM falls short of humans, for example 58% against 70% on emotion understanding 2501.08579 tab. 1. The tasks differ, so the numbers do not contradict each other; the disagreement is over what counts as evidence.
• The Physics of Agents card reports 75.1% to 86.3% one-step accuracy on held-out votes 2608.16578 tab. 1. Those results are for simulated personas on fixed questions, and the authors say they are not a model of human opinion 2608.16578 §7. A reader should not put the two accuracy figures side by side as if they measured the same thing.

The variant cards share no numeric result. The papers themselves have inconsistencies that an implementation has to resolve:

• AgentReview's text and tables disagree in places. The text gives the authoritarian AC's agreement as 69.8%, while 2406.12708 tab. 2 gives 69.41%. The text calls the drop with more malicious reviewers "consistent", but the final averages in 2406.12708 tab. 5 are not monotone: 3.254 with one malicious reviewer and 3.485 with two. The abstract's 37.1% decision variation 2406.12708 §1 equals 100 minus the malicious row's agreement in 2406.12708 tab. 2, a derivation the paper does not state.
• The COVID-ABS age distribution is β(2, 4) in the parameter table 2006.10532 tab. 2 and β(2, 5) in the text 2006.10532 §3.2.
• The COVID-ABS personal GDP share is listed as 0.04 but defined as 1 minus the public and business shares, which gives 0.94 2006.10532 tab. 2 2006.10532 §3.2.
• Artificial Leviathan gives covetousness a spread of 5 in its trait draw 2406.14373 §3.2, but its prompt gives a range of 1.1 to 1.6 2406.14373 app. A. The paper does not say how a draw maps to that range. Its text also gives two rules for who may concede: any target, in §3.3, or only a target facing a "controller" in §4 2406.14373 §3.3 2406.14373 §4. Its rate tables use 85 runs 2406.14373 §7.2, while its memory-depth correlation uses N = 83 2406.14373 §7.4, and the pooling is not explained.
• The Turing Experiment paper defines the k-choice probability with normalization over valid completions 2208.10264 §2. Its card records that the released Milgram judge compares an unnormalized probability with 0.5, so the code and the definition differ on that rule (see that card's Paper vs code notes).

The papers do not resolve these. Pick a value, record the choice, and expect results to depend on it.

Papers

• COVID-ABS: an hourly agent-based SEIR model with households, businesses, a government and a health system, with seven social-distancing scenarios. Author-reported, not validated against data.
• Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies: Turing Experiments that prompt a language model to act as many zero-shot participants in four human-subject studies. Author-reported; the participants do not interact.
• Artificial Leviathan: Exploring Social Evolution of LLM Agents Through the Lens of Hobbesian Social Contract Theory: nine language-model agents farm, rob and trade over food and land, and the runs reach a single sovereign. Author-reported; one proprietary model, no public code.
• Physics of Agents: Statistical Mechanics Predicts Collective Behavior of AI Agents: 32 persona-conditioned LLM agents vote over rounds on a signed graph, with a fitted Ising-style update. Author-reported; simulated personas and a small question set.
• AgentReview: Exploring Peer Review Dynamics with LLM Agents: LLM reviewers, an author and an area chair simulate ICLR-style review, with one trait varied at a time against a baseline. Author-reported; no comparison with real review outcomes.
• LLM-based Human Simulations Have Not Yet Been Reliable: a position paper on LLM stand-ins for people and a validation loop for them. No experiments of its own; the loop is not evaluated.