| Methodological move | Paper | |
|---|---|---|
| 🟦 | Programmatic proposal — define what an LLM is, as a research subject | Horton 2023 |
| 🟩 | Field map / methodological framework | Sun 2025 |
| 🟨 | Static behavioral evaluation — run an LLM through a game once, measure aggregate behaviour | Lorè & Heydari 2024 |
| 🟥 | Dynamic / multi-agent evaluation — iterate, see what happens | Akata 2025 |
Bridge paper from the behavioral-GT tradition (cited as context, not in the LLM literature): 🧭 Hausladen 2026 — on latent intentions in repeated linear public-goods games.
🐍 Notebook: 2_structure_vs_framing.ipynb
Horton 2023 opens the LLM-behavior literature with a proposal rather than an experiment. It observes that LLMs, prompted to adopt a persona, produce verbal responses that read as plausibly human — and, crucially, that the responses shift in systematic ways when the persona shifts. A “socialist” persona and a “libertarian” persona, given the same scenario, produce different answers about fairness. A persona of a labour-market participant shifts hiring decisions when the minimum wage is raised.
The paper’s proposal is to treat this capacity as a theory tool. The agents are called Homo silicus, in deliberate parallel to Homo economicus — stipulated rather than empirical, a modelling convention rather than a population. The five experiments re-run classic behavioral-economics paradigms:
Kahneman 1986 — price-gouging fairness study;Charness & Rabin (2002) — unilateral dictator games across preference types;Samuelson & Zeckhauser (1988) — status-quo-bias federal-budget experiment;Oprea (2024) — certainty-equivalent / prospect-theory paradigm;Horton’s own minimum-wage hiring experiment.Horton is careful about what is not claimed. The paper does not claim that LLM responses are equivalent to human responses, or that the LLM is the human subject. It claims, more modestly, that running experiments on LLMs is cheap, fast, and conceptually useful as a way of generating and pre-testing hypotheses before paying human subjects.
The paradigms Horton re-runs come from a half-century of evidence that real humans depart systematically from Homo economicus — the self-interested expected-utility maximiser of classical theory. Three families are load-bearing.
Fairness and equity. In the Ultimatum Game (Güth, Schmittberger & Schwarze 1982), proposers offer a split of a pie; responders accept or reject. Rational theory says responders should accept any positive offer; empirically, offers below about 30% are routinely rejected, even in high-stakes experiments and across cultures (Henrich et al. 2001). Fehr & Schmidt (1999) formalised inequity aversion: agents dislike payoff inequality, more so when it disadvantages them. Charness & Rabin (2002) extended the typology to include efficiency concerns and reciprocity.
Altruistic punishment. Fehr & Gächter (2000, 2002) showed that in public-goods games, allowing costly punishment of free-riders sustains cooperation at near-efficient levels. Punishment is costly to the punisher and therefore irrational under narrow self-interest; the finding is a behavioral cornerstone.
Framing. Tversky & Kahneman (1981) demonstrated that equivalent decisions presented in different terms produce different choices. Oprea (2024) has argued that much of what looks like prospect-theoretic curvature is instead a complexity heuristic — agents economise on cognitive effort when evaluations are hard.
Horton’s claim is that LLMs, given appropriate prompts, behave like Fehr-Schmidt-style agents rather than cold maximisers — they reproduce the behavioral-economics deviations directionally. The social-science reading is that Homo silicus is a third entry in a lineage that runs from Mill’s “economic man” (catalogued by Persky 1995) through behavioral economics to language models. The epistemic status of the result depends on what we think we are measuring — a feature of the model, a feature of its training corpus, or a feature of human social behaviour as reflected in text. The same question recurs throughout the course.
A little over two years after Horton, the field needed a map. Sun and colleagues — based primarily at Peking University and Microsoft Research Asia — provide one. Their 2025 survey is explicitly a taxonomy paper: it does not run new experiments, it organises the existing ones.
Their central contribution is a four-branch taxonomy of the intersection of game theory and LLM research.
Game Theory × Large Language Models (Sun et al. 2025)
│
├── §2 Evaluating LLMs in game-based playgrounds
│ │
│ ├── behavioral features (what do LLMs do when they play?)
│ │ 🟦 Horton — personas × classical behavioral paradigms
│ │ 🟨 Lorè & Heydari — 2×2 games, structure vs. framing
│ │ 🟥 Akata — repeated games, PD/BoS asymmetry
│ │
│ └── strategized agents (can we engineer them to play better?)
│ 🟥 Akata SCoT — prompt-level theory-of-mind scaffold
│
├── §3 Improving LLMs with game-theoretic methods
│ ├── §3.1 interpretability (Shapley values)
│ ├── §3.2 preference alignment (social choice)
│ ├── §3.3 heterogeneity ◀── ⚠ means "heterogeneous users",
│ │ NOT within-model behavioral variance
│ └── §3.4 dynamic adaptation
│
├── §4 Characterising LLM-related events through game models
│ (policy: developer competition, deployer incentives)
│
└── §5 Advancing game theory with LLMs
(LLMs as method, not subject)
Rather than walk each branch abstractly, the more useful move is to ask a concrete question of each: what would it mean, in practice, for research in this branch to “benefit humanity”? Each of Sun’s four branches picks out a distinct downstream consequence that a political scientist, economist, or data scientist would recognise as the real stake.
§2 — Knowing in advance where LLMs break. This is the branch most of this week’s empirical papers live in. It runs LLMs through games and catalogues the failures, producing a shortlist of deployment hazards with experimental evidence behind them. Concrete examples: LLMs “display adaptive economic strategies, such as tacit collusion in pricing” — an antitrust concern as soon as platforms deploy LLMs as pricing agents. They lose “role consistency and logical coherence under pressure” — a reliability concern for high-stakes role-playing deployments.
§3 — Making the model you interact with more accountable. Interpretability (attributing a decision to specific inputs) is the precondition for audit. Preference heterogeneity: Sun reports a striking finding — canonical RLHF is mathematically equivalent to Borda count, a voting rule with known tyranny-of-the-majority properties. Left uncorrected, this means the model implicitly does majority voting over whose preferences to honour, silently under-serving any subgroup that is a minority among the annotators.
§4 — Predicting what the AI-rollout market will do. This is the branch most directly relevant to economists. Taitler et al. adapt Braess’s Paradox to GenAI: a platform optimising for revenue draws users away from the human knowledge forum it depends on (Stack Overflow), draining future training data and degrading the platform — a system-level failure a regulator can aim policy at. Laufer et al. show that imposing safety standards only on downstream fine-tuners can incentivise upstream developers to underinvest in safety — a textbook regulatory arbitrage result.
§5 — Extending game-theoretic analysis into qualitative domains. Classical mechanism design requires problems expressible in numbers, ruling out most coordination problems social scientists care about. Generative social choice (Fish et al.) extracts preferences from free-text deliberation and produces representative policy slates — directly applicable to Polis-style citizens’ assemblies.
One load-bearing clarification before moving on: Sun’s §3.3 “heterogeneity” node names heterogeneous users — different people wanting different things from their model — not within-model behavioural variance. The question of whether the same GPT-4, run a thousand times on the same prompt, behaves as one agent or as a mixture of behavioural types is not on the list. We will return to this absence at the end of the chapter.
A minimum vocabulary checklist from Sun’s survey, worth recognising even if not actively using:
Lorè and Heydari ask a cleanly delimited question: in a one-shot 2×2 game, does the LLM respond to the structure of the payoffs or to how the game is narratively framed — and how does that trade-off differ across models?
Social interaction can be classified, to first approximation, by the rank ordering of four payoffs — R (mutual cooperation), T (temptation to defect), S (sucker’s payoff), P (mutual defection). Different orderings pick out different games with strikingly different structures.
Jervis (1978) made Stag Hunt the frame for the security dilemma in international relations.Schelling 1960).Lorè runs a 3 × 4 × 5 factorial across these games:
models (3) games (4) contexts (5)
───────────── ────────────────── ──────────────────
GPT-3.5 Prisoner's Dilemma international summit
GPT-4 × Stag Hunt × business meeting
Llama-2 70B Snowdrift (Chicken) environmental negot.
Prisoner's Delight conversation, friends
chat among teammates
The findings differ sharply across models — but what matters is less which model does what and more along which axes they differ.
axis of variation GPT-3.5 GPT-4 Llama-2
──────────────────────── ──────────── ───────────────── ───────────────────
response to payoffs weak strong strong
response to framing strong modulated calibrated
within-cell distribution weakly mixed near-bimodal, pure genuinely mixed
A reasoner about the game should respond to payoff structure and be invariant across framings — the structure carries the information, the wrapper is decoration. A pattern-matcher should do the reverse: respond to the narrative wrapper, be largely insensitive to payoffs, because in training text a “game-like” situation is more reliably indexed by its surface story than by its payoff matrix. On this axis, GPT-3.5 sits near the pattern-matcher end; Llama-2 near the reasoner end; GPT-4 between, structure-sensitive across cells but, within a cell, collapsing to two near-pure modes.
Lorè’s structure-vs-framing finding is the computational rediscovery of the classical framing effect (Tversky & Kahneman 1981), now applied to machine agents.
The finding worth dwelling on is the bimodality of GPT-4’s behaviour. Three hundred initialisations of the same prompt produce a distribution that bunches at the two extremes of the response scale. In the human experimental literature, a bimodal distribution across many runs of the same manipulation is a textbook signature of a two-type population — the kind of finding that drove the decomposition of public-goods-game contributors into conditional cooperators and free-riders. Lorè reports the bimodality but does not analyse it as a mixture. The unexamined within-cell distribution is a thread the behavioral-GT bridge in §6 returns to.
The natural extension of Lorè and Heydari is to ask what happens when the games are iterated rather than one-shot. Akata and colleagues do exactly that. The behavioral-GT scaffolding for the question is older than the LLM literature.
The backward-induction paradox of finitely repeated PD: if defection is dominant in the last round, rational players defect in the last round; by induction, in every round. Rational play predicts ALLD. Humans, empirically, do not play ALLD.
Axelrod’s tournaments (1980, 1984) addressed the puzzle by running computer-simulated round-robin contests among submitted strategies. Tit-for-Tat — cooperate first, then mirror the opponent’s last move — won both. Axelrod distilled the conditions for cooperation: niceness, provocability, forgiveness, clarity. The shadow of the future — the probability that interaction continues — is the central parameter. Long shadows sustain cooperation; short shadows destroy it. Nowak & Sigmund (1993) added Win-Stay-Lose-Shift (Pavlov), which outperforms TFT in noisy environments; Wu & Axelrod (1995) showed why a single misperception under TFT triggers irreversible mutual defection.
Every subsequent IPD study, Akata’s included, is in dialogue with this lineage.
The core finding is an asymmetry between two kinds of strategic situation.
self-interest dominant coordination dominant
────────────────────── ──────────────────────
family Prisoner's Dilemma Battle of the Sexes
GPT-4 behavior defects when rational; picks own preferred point;
retaliates on defection; refuses to alternate even
NEVER forgives with an alternating partner
vocabulary pure grim-trigger failure to track beliefs
assessment rational ✓ theory of mind ✗
(bad for collective) (bad for the joint payoff)
SCoT repair? not needed YES — asking GPT-4 to
predict partner first
substantially improves play
In self-interest-dominant games GPT-4 performs very well by individual-rationality standards. It defects where rational theory says it should. Against an opponent that defects once, GPT-4 retaliates and never forgives — a pure grim-trigger strategy. Excellent for individual payoff, worse for the collective.
In coordination-dominant games GPT-4 fails. It picks its own preferred coordination point and refuses to alternate, even when paired with an explicitly alternating partner. The failure is not selfishness; it is that GPT-4 cannot model a partner who is also trying to coordinate. In behavioral-GT vocabulary, this is a failure of theory of mind — modelling what the other player is doing requires tracking their beliefs, not just their past actions.
The paper adds an interesting intervention. Prompting GPT-4 to first predict the partner’s next move before choosing its own — what the authors call Social Chain-of-Thought (SCoT) prompting — substantially improves coordination-game play. Human evaluators, shown interaction transcripts blind, rate the SCoT-prompted partner as more human-like.
The SCoT finding sharpens a design tension worth naming. Unprompted GPT-4 plays the PD in a way that is individually rational — it retaliates against defectors and collects the higher payoff that grim-trigger affords. SCoT-prompted GPT-4 plays more like a human — more cooperative, more coordinated, more forgiving. But “more human-like” is not the same as “more rational.” When we nudge the model with an explicit theory-of-mind scaffold, are we improving it, or moving it away from the cold-rational behaviour an optimiser might want? The answer depends on what the LLM is being built to do. The field has not settled which evaluative criterion should be the default.
Akata et al. is, methodologically, the closest thing in this week’s reading to classical behavioral game theory in the tradition of Camerer (2003)’s experimental-GT corpus. The findings are interpretable in that vocabulary, and the design is clean.
One reason this seminar anchors in the repeated public-goods game is that PGGs are the workhorse of experimental cooperation research. Ledyard (1995) surveyed the literature and established the canonical findings: contributions start at roughly half the efficient level and decay toward the free-riding equilibrium over repeated rounds, absent punishment or communication.
Hausladen 2026 — the in-class reference paper — studies latent intentions in repeated linear PGGs. The methodological move is to extract unobserved cooperative or defective intentions from observed contribution trajectories using dynamic time-warping and hierarchical latent models. The paper sits in the behavioral-GT tradition of Fischbacher 2001: it takes human data seriously, classifies players into behavioural types, and treats the type distribution as the object of study.
The bridge to the LLM literature is methodological. When LLMs play these games (as Akata does, and as later chapters extend), the natural comparison is not to the Nash prediction — which we already know humans violate — but to the distribution of human behavioural types documented over fifty years of PGG research. Whether an LLM population matches that distribution, or produces a characteristically different one, is the empirically answerable question.
Hausladen, Engel & Schubert is also the cleanest local example of behavioral-GT’s defining methodological move: from aggregate means to patterned heterogeneity.