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Decision theory × Buddhist and Daoist thought · research synthesis · 2026-09-27

Dharma and Daoist Concepts in Decision Theory: Computable Bridges, Boundaries, and a Falsified T1 Threshold

Macheng Shen (research initiator), in collaboration with an AI research assistant

1. Plain-language conclusion

It is intuitively tempting to understand “enlightenment” as knowing more and more, but more complete knowledge does not automatically loosen attachment. The more defensible H-Bridge says that increased understanding can reduce inner conflict only when a model can also see its own limits and allows knowledge that “some things are uncontrollable” to revise existing preferences. The part of wu wei most amenable to formalization is using the environment’s own dynamics and applying only the necessary control at critical points—not doing nothing. The unity of knowledge and action can be divided into three researchable layers: perception and action share an objective; skilled action is distilled from planning; and some causal knowledge can be acquired only through intervention. The toy experiments support the H-Bridge’s conditional interaction and a trade-off at moderate self-precision, but those successes belong only to the models specified in advance. By contrast, the wu-wei experiment did not meet its preregistered success threshold, so its attractive energy-saving result cannot be presented as validation. Mathematics can clarify structure and generate counterexamples, but it cannot define “pure awareness,” the moral source of conscience, complete intentionlessness, or existential suffering. The formalization here should be treated as a testable map, not as religious experience or the traditions themselves.

2. Concept-by-concept correspondence

Traditional conceptFormal objectStrengthMain distortion
Wu weiLMDP: reweight passive dynamics by desirability, pricing control deviation with KLstrong control problemStill presupposes an objective function and cannot express “letting go even of the objective”
Unity of knowledge and actionControl as inference; planning distillation; the causal difference between observation and interventionstrong to partialCaptures structure but loses conscience, mind-as-principle, and moral motivation
EnlightenmentTask-relative world-model error, preference precision, and its updateabilitypartial“A complete model is enlightenment” is too strong; knowledge can also intensify conflict
No-selfA latent self-variable and its precision (gamma_{self})partialReducing rigid priors is not realizing no-self, nor is it deleting the agent
Attachment, craving, and sufferingHigh preference precision and persistent risk terms in uncontrollable situationspartialCan only approximate the conflict of frustrated desire; cannot exhaust aging, illness, death, or pervasive conditioned suffering
EmptinessModel classes, coarse-graining, and statistical non-identifiabilityrhetorical to partialEngineering-level “lack of intrinsic essence in representations” cannot replace Madhyamaka argument; this formalization is itself not an ultimate description
Dependent originationStructural causal models and interventional distributionspartialFixes variables and causal edges and cannot carry all the ethical and ontological meaning of dependent origination
Calm and insight, meta-awarenessSecond-order inference over the allocation of attentional precisionpartialA computational proposal, not a confirmed neural mechanism of meditation
Sudden and gradual awakeningContinuous evidence accumulation and a discrete flip in the MAP modelpartialDoes not include liberation, ethical transformation, or lineage recognition
Middle WayA Pareto frontier under explicit objectivesrhetorical to partialNot a midpoint parameter value or generic compromise
The Dao follows what is natural; highest goodness is like water; reversal is the movement of the DaoGenerative processes, compliant control, and negative feedbackrhetoricalWithout independent predictions, these are merely renamings in modern terminology

3. The enlightenment tension: A / B / Bridge and T3

H-A: epistemic completeness

The more thorough the exploration and the more accurate the model, the lower the conflict. The problem is that factual knowledge does not determine preferences: knowing more accurately that a bad outcome is unavoidable may make fixed attachment more painful.

H-B: release of attachment

Reducing attachment itself is sufficient to lower conflict, independent of increased understanding. The problem is that if one cannot see one’s own impulse to control and its consequences, preferences are difficult to revise in a targeted way.

H-Bridge: conditional bridge

Increased understanding leads to release only when both bridge factors are present: the model can represent its own modeling and control limits; and preferences can be updated by evidence of uncontrollability.

$$A\Rightarrow B\quad\text{only when}\quad M\supseteq\text{its own modeling process}\;\land\;\gamma_C\text{ can update with evidence of uncontrollability}$$

In a generative toy experiment with 16 conditions and 800 runs per cell, T3 shows a clear interaction: under the complete bridge, high exploration changes distress by −1.509; without the bridge, the change is +4.369; the difference-in-differences is −5.878. The prespecified kill condition—an exploration-effect difference of less than 1 inside versus outside the bridge—was not triggered. This counts against the unconditional sufficiency of H-A and supports the distinguishable structure of H-Bridge within this model; because the mechanism was written into the model according to H-Bridge, the result is not independent validation of a real psychological mechanism.

T3: factorial results for exploration intensity, preference updating, and the self-modeling metavariable
T3: high exploration lowers the model’s conflict readout only when both bridge factors are present.

4. Wu wei: LMDP and T1’s negative result

A linearly solvable Markov decision process writes the cost at each step as a state cost plus a KL cost for deviation from passive dynamics:

$$J(u)=\mathbb E_u\sum_t\left[q(s_t)+\beta D_{\mathrm{KL}}\!\left(u(\cdot\mid s_t)\Vert p_0(\cdot\mid s_t)\right)\right],\qquad u^*(s'\mid s)\propto p_0(s'\mid s)z(s')$$

This yields a precise, weak engineering version: good control does not reduce action to zero; it reweights the natural flow and concentrates control where it genuinely changes reachable outcomes. It can distinguish compliant control, random drift, and sustained brute force.

T1 was falsified by its preregistered threshold. The best point in the scan had a success rate of about 0.927 < 0.95. Therefore, even though its KL was only about 0.043 times that of brute force, the prespecified “wu-wei point” cannot be claimed. The share of control concentrated in the barrier region was 0.286, above the random baseline of 0.083, and the curve showed a descriptive bend, but these secondary phenomena cannot override failure on the primary threshold.
T1: scan of success rate and KL control cost
T1: highly economical in control cost, but the success rate did not cross the prespecified 0.95 threshold.

5. Three layers of the unity of knowledge and action

  1. Unified objective: active inference places state estimation and action selection within the same optimization objective. “Knowledge” and “action” constrain each other computationally rather than forming completely independent sequential modules.
  2. Amortized distillation: a slow planner produces a policy, which is then distilled into a fast parametric policy. Repeated practice compiles explicit deliberation into fluent skill, explaining the difference between “knowing how to do it” and “being able to do it.”
  3. Interventional knowledge: under confounding, observation (P(Y\mid X)) generally cannot identify the intervention (P(Y\mid do(X))). Some causal knowledge must therefore be acquired through action; this is a rigorous weak version of “knowing without acting.”

These three layers do not formalize what Wang Yangming called conscience. They describe unified control, skill formation, and causal identification; they neither prove that moral knowledge is innate nor derive “mind is principle” from performance metrics.

6. T2: the commitment–recovery trade-off in self-precision

T2 scans (gamma_{self}\in\{0,0.35,1,3\}) in a POMDP whose rules change. Moderate precision at (gamma_{self}=1.0) produces the highest total return, 40.029: when precision is near zero, recovery is fast but sustained commitment is harder to form; when precision is high, commitment is strong but recovery after the rule reversal is slow and cumulative risk is higher. The preregistered kill condition—the endpoint return is highest, or precision affects neither recovery nor commitment—was not triggered.

Readout limitation: futile_control_rate equals 1 under every condition because an action must still be chosen at each step during the uncontrollable phase. This metric has degenerated and has no discriminative power; the conclusion depends only on cumulative risk, recovery, commitment, and total return.
T2: commitment and recovery trade-off under different levels of self-precision
T2: intermediate precision achieves the best total return in this toy task, but that does not validate “no-self.”

7. Where formalization breaks

8. Disagreements between the two analyses, and the general governance question

On “emptiness”

One analysis treats model dependence, coarse-graining, and non-identifiability as a partially operational correspondence; the other emphasizes that this remains an epistemic analogy, and that Madhyamaka would go on to question whether “information” itself has ultimate standing. The merged position is that the engineering correspondence is usable, but its strength must not exceed “partial,” and it cannot be used to establish a new substantialism.

The blind spot in “wu wei”

The formal draft highlights the strong mathematical structure and killable experiment of an LMDP; the critical draft emphasizes that its objective function never disappears. The merged position is that the correspondence is strong for “control that deviates less from natural dynamics,” but only partial or rhetorical for intentionlessness, spontaneity, and political ethics in the classical context.

Tight coupling does not imply concentrated power

Tight perception–action coupling within an individual or single system is a design for rapid information return; concentrating perception, judgment, execution, and review in the same node of organizational governance weakens correction and accountability. The two can coexist, but layer boundaries must be explicit: the execution loop can be tight while authorization and verification remain separate; a locally unified objective cannot automatically justify institutional centralization.

9. Falsifiable predictions

  1. Wu-wei control: if the objective aligns with a natural attractor, there should be a high-success, low-KL control point, with control cost concentrated near the barrier. T1 failed because its 0.927 success rate did not reach 0.95.
  2. Self-precision: moderate (gamma_{self}) should outperform both endpoints while showing a commitment–recovery trade-off; if an endpoint is best or neither readout changes, the operationalization fails. T2 has not yet triggered this condition.
  3. H-Bridge: exploration’s effect in reducing conflict should depend on “preferences are updateable” and “the model includes its own limits” holding simultaneously; if the effect difference inside versus outside the bridge is less than 1, the design is not distinguishable. T3 has not yet triggered this condition.
  4. Interventional knowledge: in tasks with confounding, active interveners should have lower causal error than pure observers with equal samples; if there is no difference, the causal weak version of the unity of knowledge and action fails.
  5. Distillation: distillation after planning should reduce action latency while retaining transfer performance; if there is no speed benefit or transfer degrades substantially, the skill-layer mapping fails.
  6. Sudden–gradual mechanism: continuous evidence can accompany a discrete flip in MAP structure selection; if pure parameter learners show the same jump, or the structural model shows no threshold behavior, the explanation loses discriminative force.
  7. Meta-awareness: updateable second-order precision should recover calibration after a rule change faster than fixed attentional gain, without impairing discrimination during stable periods; otherwise the modeling proposal is weakened.

10. Do-not-claim list

11. Where conscience comes from: theory of mind, games and karma

Updated · 2026-09-27 The round-2 preregistered models C1–C4 and the post-hoc exploratory arm are complete; all round-1 verdicts remain unchanged.

Plain-language conclusion: At high noise (25%) or when mimics are present, none of the tested cooperation mechanisms—including conscience—survives evolution. At moderate noise (10%), only TFT remains above the preregistered veto line, retaining about 20%; fixed-weight conscience remains below 10% (about 8%), and WSLS about 6%. Without noise, conscience (about 41%) and TFT (about 37%) both survive. Conscience is therefore not a sufficient condition for cooperation, but it is not uniquely weak.

The submitted intuition and a one-shot theorem

A reader-submitted intuition worth testing is that, among agents sharing similar models of minds and meeting repeatedly, conscience may be an internalized tool for escaping the Prisoner’s Dilemma. We treat this neutrally as a research hypothesis, not a conclusion. The strict boundary is: in a one-shot Prisoner’s Dilemma, if utility contains only one’s own material payoff, theory of mind (ToM) improves prediction of the other player but does not alter dominant defection. Knowing that “the other is like me” does not itself put that person’s welfare into my objective.

With other-regard (U_i=\pi_i+w\pi_j), the general threshold for cooperation against either action is:

$$w\geq\max\left\{\frac{T-R}{R-S},\frac{P-S}{T-P}\right\}.$$

Replace “≥” with “>” for strict preference. When the partner cooperates, (w=1) suffices iff (2R>T+S). When the partner defects, it additionally requires (T+S\geq2P) (or (T+S>2P) for strict preference), which the definition (T>R>P>S) does not guarantee. For (T=4,R=3,P=2,S=0), the agent is exactly indifferent.

Karma in four layers only

LayerLimited formal counterpartBoundary
K1 social reputationObserved and assessed conduct feeds back through third-party help: indirect reciprocityRequires observers and a same-generation public reputation; not karma as a whole
K2 intention-sensitive assessmentObservers infer intention before judging; norms such as standing can be extended this wayNeeds an explicit ToM-accuracy and misclassification model; AN 6.63 identifies karma with intention (cetanā)
K3 internal dispositionsA state with memory and path dependence, or hysteresisRound-1 preregistered hysteresis failed; a behavioral state is not a stream of consciousness
K4 doctrinal karmic resultNo reliable game-theoretic counterpartThe karmic results discussed in MN 135 are not formalized here

Round-1 preregistered results

Round-1 noisy repeated Prisoner's Dilemma results
Repeated game: fixed-weight conscience hits the kill line at 10% noise.
Round-1 indirect reciprocity results
Indirect reciprocity: standing passes the limited comparison with image scoring.
Round-1 hysteresis results
Hysteresis: the shape appears, but the preregistered discrete criterion fails.
Round-1 anonymous help and anti-cartel results
One-shot anonymous help and anti-cartel behavior pass the preregistered proximate-expression criteria.

Round-2 preregistered results

Round-2 C1 evolutionary-retention results
C1: conscience weights were not retained under selection, while mimics flourished.
Round-2 C3 social-hysteresis results
C3: the social loop met its criterion, but only as a mechanism demonstration.
Round-2 C2 intention-reputation results
C2: intention-based assessment improved cooperation only narrowly, at high execution error and high inference accuracy.
Round-2 C4 cartel results
C4: broader concern did not change the structure in which unilateral exit could not prevent harm.

Post-hoc exploratory: conditional conscience weight (not preregistered)

Post-hoc exploratory / 事后探索: This arm was added after seeing both rounds. It was not preregistered and cannot overturn or rewrite any verdict above. The conditional-weight type ended at 0.82%, versus 0.38% for the fixed-weight type, while ALLD reached about 97%. At most, this suggests that lowering weight in response to an opponent’s reputation may reduce exploitation slightly; it does not support stable cooperation.

Final population share by strategy

Arm / environmentMean final or late population share
Round 1 · noise 0conscience 41.3%; TFT 36.6%; WSLS 21.5%; ALLD 0.6%
Round 1 · noise 0.10conscience 8.3%; TFT 23.4%; WSLS 5.7%; ALLD 62.6%
Round 1 · noise 0.25conscience 0.7%; TFT 0.8%; WSLS 0.7%; ALLD 97.7%
Round 2 C1 · prep 0.25, a 0.8conscience implant 0.55%; conscience erode 0.75%; SELF_TOM 0.16%; TFT 0.07%; WSLS 0.06%; ALLD 22.51%; SELF 52.21%; MIMIC 23.56%
Round 2 C1 · prep 0.25, a 1.0conscience implant 0.53%; conscience erode 0.78%; SELF_TOM 0.19%; TFT 0.07%; WSLS 0.07%; ALLD 41.16%; SELF 21.91%; MIMIC 35.12%
Round 2 C1 · prep 0.50, a 0.8conscience implant 0.48%; conscience erode 0.48%; SELF_TOM 0.09%; TFT 0.05%; WSLS 0.06%; ALLD 29.35%; SELF 37.98%; MIMIC 31.35%
Round 2 C1 · prep 0.50, a 1.0conscience implant 0.46%; conscience erode 0.53%; SELF_TOM 0.08%; TFT 0.06%; WSLS 0.07%; ALLD 26.28%; SELF 37.03%; MIMIC 35.38%
Post-hoc armconditional-w 0.82%; fixed-w 0.38%; TFT 0.6%; WSLS 0.5%; GTFT 0.5%; ALLD 97.2%
Scope limitation: WSLS normally sustains cooperation in noisy repeated games, yet here it fell to about 6% at 10% noise and near zero under 25% high noise or with mimics, showing that these environments are unusually hostile to cooperation. At 10% moderate noise, TFT still retained about 23%, above the preregistered 10% veto line; fixed-weight conscience retained about 8%, below that line. Without noise (round 1, noise 0), conscience (about 41%) and TFT (about 37%) both survived. The claim that no tested mechanism survives therefore applies only to the tested environments with 25% high noise or mimics, not to noisy environments or cooperation in general.
Post-hoc exploratory conditional-conscience-weight results
Post-hoc exploration: conditional weight modestly exceeded fixed weight, but both were overwhelmed by roughly 97% ALLD.

Three tensions with classical texts

  1. Mencius’s three exclusions in the child-at-the-well passage: the impulse is not to gain favor with the parents, win praise from the community, or avoid the sound of distress. At the proximate level these exclude direct reciprocity, reputational return, and mere relief of one’s own discomfort.
  2. The scope gradient in Wang Yangming’s “Questions on the Great Learning”: unity extends from a child to birds and beasts, plants, and finally tiles and stones. At the endpoint there is no mind to model and no possible reciprocity, so similarity weighting (w s_{ij}) goes to zero while the classical claim continues—an explicit boundary of the model.
  3. Zhuangzi’s “Even robbers have a Way”: cooperative norms can serve thieves and cartels, so cooperation is not morality. Similarity weighting also naturally predicts parochial altruism: favoring similar others can coevolve with intergroup conflict.

Proximate, ultimate, and an explicit disagreement

An ultimate account asks why a tendency with (w>0) might have been retained through selection, partner choice, or reputation. A proximate account describes the person directly experiencing compassion, shame, or moral judgment now, without calculating repayment. A commitment-device account can reconcile those levels, but it does not cover beneficiaries who cannot repay, tiles and stones, or normative authority. The two preregistered rounds sharpen the boundary: fixed weight failed in round 1's noisy environment, and evolvable weight did not establish in round 2. Constructed social hysteresis and intention-based assessment demonstrate limited functions of memory and intention discrimination, but do not overturn the evolutionary kills. The commitment function and broader hysteresis analogy remain mechanism claims for further tests, not substitutes for these empirical verdicts.

The account can also predict the opposite of extending innate knowing (zhi liangzhi): an evolutionary/commitment story often predicts that, once people know an interaction is one-shot, reflection weakens intuitive cooperation. Rand et al. (2012) reported that direction, but Bouwmeester et al. (2017) did not reproduce it in a multilab registered replication, so its empirical status is uncertain. The Wangian prediction instead says reflection that removes selfish obscuration strengthens conscience.

Origin is not justification. Even if evolution or games explain why a conscientious tendency appeared, that does not show it ought to be followed; discovering an instrumental origin does not refute its normative value either.

Do not claim from this section

12. References

Only entries that already had links in the two research drafts are listed. “Verified” retains the drafts’ verification labels; this synthesis did not revisit every external page. All others are marked “unverified.”

Math primer for readers

Reader’s primer: the “hard concepts” on the Dharma × decision theory page

For whom: readers with practical AI experience and a deep interest in Buddhist and Daoist thought, but no mathematics degree. How to use it: each entry first states literally, in 1–3 sentences, what the concept is (without substituting metaphor for mechanism), then gives 1–2 strong introductory resources, preferably free. Use Ctrl+F for unfamiliar terms on the page. Source verification: every link was tested on 2026-09-27. The “free” status of items marked ⚠️ is unverified.

One reminder: all of these are tools. Being expressible as a formula does not mean a concept captures what actually happens in practice—the page’s section on where formalization fails matters just as much.

I. Describing an agent making decisions in a world

Markov decision process (MDP) A format for a decision problem: there is a set of states; at each step an agent chooses an action; the environment moves probabilistically to a new state and gives a reward; the goal is a rule (policy) saying what to do in each state so as to maximize long-run cumulative reward. “Markov” means the next step depends only on the current state and action, not on earlier history.

Partially observable MDP (POMDP) An MDP in which the agent cannot see the true state and receives only noisy observations. It must maintain a probability distribution over where it may be (a belief) and act on that belief. Active inference and experiment T2 on this page use this format.

Reward prediction error (RPE) The reward actually received minus the reward expected. Reinforcement learning uses it to update expectations; in neuroscience, dopamine-neuron firing correlates with this quantity in many experiments. The page stresses: suffering ≠ RPE.

II. Probability and belief

Bayesian updating A rule for revising belief: the new belief (posterior) is proportional to the old belief (prior) times the probability of the present evidence if the hypothesis were true (likelihood). Evidence that a hypothesis made very surprising reduces its weight more strongly.

Prior precision Precision is inverse variance: how certain a belief is and how resistant it is to evidence. A high-precision prior outweighs conflicting observations; a low-precision one is easily revised. γ_self and γ_C on the page are precisions of priors about the self and preferred outcomes.

Maximum a posteriori (MAP) / Bayesian model comparison MAP selects the candidate with highest posterior probability. Model comparison treats the model structure that best explains the data as something to infer; evidence may accumulate continuously while the top-ranked model changes discretely at one moment (used here to characterize sudden and gradual awakening).

KL divergence A number measuring information lost when distribution Q approximates distribution P: zero when they are identical and larger when they differ; it is asymmetric. This page defines “control cost” as the KL divergence between actual behavior and the natural distribution when nothing is done.

Solomonoff prior A theoretical “universal prior” assigning probability to every possible law of a world, with higher probability for laws having shorter descriptions (shorter generating programs). It has elegant convergence theorems but is uncomputable and serves only as a theoretical reference. The page lists “Dao = Solomonoff prior” only as a rhetorical correspondence.

Model class, coarse-graining, identifiability A model class is the family of candidate models one allows; coarse-graining merges many detailed variables into fewer macroscopic ones; non-identifiability means two distinct internal structures generate exactly the same observations and cannot be distinguished from data alone. The page uses these as a partial engineering correspondence to emptiness (strength: only “partial”).

III. Writing “action” as “inference”

Active inference / free-energy principle A theoretical framework in which an agent has a generative model of how observations arise and reduces variational free energy in two ways: revising beliefs (perception) and changing the world so observations match expectations (action). Policy selection uses expected free energy, containing distance from preferred outcomes (risk) and expected learning (information gain). It is a modeling framework; its status as a “law of the brain” is disputed.

Variational free energy vs thermodynamic free energy Variational free energy is a statistic about beliefs (an upper bound on a model’s surprise at observations); thermodynamic free energy is a physical system’s energy quantity. Their formulas have similar shapes, but they are not the same thing.

Meta-awareness / second-order precision Second-order inference does not infer the outside world, but how much precision to assign to one’s own attention or beliefs. The page uses it as a computational proposal for meditative stabilization and observation and for meta-awareness.

Control as inference A mathematical rewriting that introduces a virtual variable for whether a step is optimal and makes its probability grow exponentially with reward. Finding an optimal policy becomes inferring the most likely action trajectory conditional on optimality, naturally producing an entropy term that favors retaining randomness.

KL control / linearly solvable MDP (LMDP) / passive dynamics Passive dynamics describe how the system evolves if the agent does nothing. An LMDP writes each step’s cost as state cost plus the KL divergence of actual transitions from passive dynamics. The optimal control then has a closed form: passive transition times exponentiated target value, normalized. The page uses this to write part of wu wei as following natural dynamics and adding minimal control at critical points.

Risk term In expected free energy, risk is the KL divergence between outcomes expected under a policy and preferred outcomes. The more rigid the preference and uncontrollable the outcome, the longer this term remains high; the page uses it to approximate conflict in “seeking but not obtaining.”

Amortized inference / distillation Amortized inference trains a network to map inputs directly to answers instead of slowly recalculating each case. Distillation trains a smaller, faster model to imitate outputs from a slower, stronger one. The page uses these to characterize the skill layer of the unity of knowledge and action.

Empowerment The maximum information (channel capacity) between an agent’s action sequence and its state several steps later. High empowerment means different actions from here can reliably reach many different futures.

IV. Causality

Causal intervention (do operator) / confounding / structural causal model A structural causal model writes the generating mechanism among variables as equations and arrows. P(Y | X) is Y’s distribution when X is observed; P(Y | do(X)) is its distribution after X is forcibly set. With confounding they generally differ, and some causal effects can be identified only through intervention (action). This yields a strict weak version of “without acting, knowledge remains incomplete.”

V. Dynamics and experimental method

Attractor / negative feedback / phase transition An attractor is a state toward which a dynamical system is drawn and then remains; negative feedback acts to push deviations back; a phase transition is a sudden qualitative change in stable state when a parameter crosses a critical value.

Hysteresis The current state depends not only on current conditions but on the path taken: when a parameter rises the system flips at a, while on the way down it flips back only at a lower b, making a loop. To distinguish true hysteresis from lag, vary the parameter arbitrarily slowly: lag disappears, whereas a true hysteresis loop remains.

Pareto frontier / “elbow” With two conflicting objectives, the Pareto frontier contains solutions where one objective cannot improve without sacrificing the other. An elbow is the point beyond which a little more cost brings almost no gain. T1 sought such a “wu-wei point” and missed its preregistered threshold.

Preregistration / kill condition Before running an experiment, state what counts as success and failure; do not change it afterward. This prevents choosing favorable interpretations after seeing results.

Difference-in-differences The treatment group’s change minus the control group’s change. T3 uses it for the interaction between the bridge condition and exploration.

VI. Multiple agents: games and conscience

Theory of mind (ToM) / level-k / I-POMDP Theory of mind models others as agents with their own beliefs, desires, and intentions, then predicts their behavior. Computational approaches often assume approximately rational planning and infer goals and beliefs backward from action (Bayesian inverse planning). Level-k limits the depth of “I think that you think…”; an I-POMDP puts models of others directly into one’s state for planning.

Nash equilibrium A strategy profile in which no player can gain by changing unilaterally while everyone else stays fixed. It need not be best for everyone, fair, or moral.

Prisoner’s Dilemma (PD) Two people choose cooperation or defection; payoffs rank as: I defect while you cooperate (T) > both cooperate (R) > both defect (P) > I cooperate while you defect (S). Whatever the other chooses, defection pays me more, so two “rational” players defect and each gets P even though mutual cooperation would give each R.

Repeated game / folk theorem When two people repeatedly play the same game and value the future enough, conditional strategies such as retaliation after defection can make cooperation an equilibrium. The folk theorem says any payoff profile giving each person at least their worst guaranteed payoff can become an equilibrium when players are patient enough—including unfair profiles.

Indirect reciprocity / reputation / assessment norm “I help you; someone else helps me”: whether to help depends on reputation, which observers assign under a norm—for example, helping a good person is good and refusing a bad person can also be good. Only a few norms sustain cooperation under error; disagreement among observers readily erodes it. The page uses this as a formal analogy for karma’s social layer.

Social preferences / inequity aversion Add others’ payoffs to the utility function. In the Fehr–Schmidt model, people dislike both having less than others and having more than others.

Kantian optimization (Roemer) Instead of asking what unilateral change benefits me while others remain fixed, ask whether I would want everyone to change their action in the same way. In a symmetric Prisoner’s Dilemma, this selects cooperation.

Commitment device An arrangement that binds one in advance against future temptation; because the commitment is credible, others become more willing to cooperate. Frank argues that moral emotions such as guilt and indignation serve this function: precisely because they do not calculate, they can be credible.

Program equilibrium If both sides submit mutually readable programs, programs like “cooperate only if the other program can be proved to cooperate with me” can cooperate in a one-shot Prisoner’s Dilemma. This requires transparent code, which humans and present neural networks do not have.

Evolutionary game / replicator dynamics Treat strategies as types reproducing in a population: a strategy earning more than average increases its share. This asks which tendencies, such as conscience weight w, are selected over time.

Sequential social dilemma (multi-agent reinforcement learning) Extend the Prisoner’s Dilemma into persistent, multi-step behavior in a grid world, such as overharvesting a commons, and use reinforcement-learning agents to study how cooperation emerges or collapses. Common additions include inequity-aversion rewards, social-influence rewards, and opponent shaping (LOLA).

Evolutionary altruism vs psychological altruism (ultimate vs proximate cause) Evolutionary altruism is defined by effects on reproductive fitness; psychological altruism by the actor’s motive (genuinely wanting to help). SEP notes that neither implies the other. This distinction is central to reconciling “conscience as a tool” with Mencius’s claim that conscience seeks no return.

VII. Safe to skip at first

Theory mainline index — Return to the site hub and grouped directory.

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