The Ten Cross-Scientific Detection-Limit Invariants
1. Sensitivity vs. Noise Floor
What “sensitivity” means in this field
In interaction-focused economics, the signal is not an individual preference but a strategic relationship: beliefs about others, conditional responses, private valuations, coordination, deterrence, or exploitation embedded in multi-agent behavior.
Sensitivity here refers to the field’s ability to detect strategic structure—how one agent’s action responds to expectations about others—against the background variability of market activity, institutional frictions, and informational asymmetry.
Sources of noise
Noise in interactive settings is both behavioral and strategic:
- Private information: valuations, beliefs, and constraints are deliberately concealed.
- Strategic randomization: mixed strategies intentionally inject noise.
- Market microstructure noise: bid–ask bounce, timing jitter, order batching.
- Institutional friction: transaction costs, rules, delays, enforcement lags.
- Selection effects: only successful, feasible, or equilibrium-consistent interactions are observed.
- Exogenous shocks: demand, supply, or regulatory changes overlapping with strategic moves.
Unlike micro choice, some noise is purposefully generated by agents to remain unpredictable.
The detection boundary
A strategic effect is detectable only if it produces systematic, non-random patterns in interactions that exceed this compounded noise floor. Below that threshold:
- Private information remains observationally hidden.
- Belief updates cannot be distinguished from random fluctuations.
- Tacit coordination appears identical to independent behavior.
- Deterrence and signaling effects blur into background volatility.
Thus, many strategic phenomena exist in theory but remain empirically latent.
Empirical manifestations of the limit
This limit appears as:
- Flat or weakly identified payoff and belief parameters.
- Inability to distinguish equilibrium selection mechanisms.
- Observational equivalence across different strategic models.
- High sensitivity of results to timing, matching, or institutional assumptions.
- Difficulty detecting collusion without explicit communication evidence.
Even rich transaction data often fails to resolve fine strategic distinctions.
Consequences for inference
Because of this limit:
- Beliefs and strategies are inferred, not observed.
- Many game-theoretic predictions are underidentified empirically.
- Causal claims about strategic intent are fragile.
- Structural models rely heavily on equilibrium assumptions.
- Policy conclusions often depend on coarse behavioral responses rather than precise strategic mapping.
The limit is intrinsic to strategic interaction, not a failure of data collection.
What lies beyond the limit
Below the sensitivity threshold lie:
- Subtle belief shifts and expectation formation.
- Weak signaling or deterrence effects.
- Tacit collusion without strong price or quantity coordination.
- Conditional strategies with small payoff differences.
These may shape outcomes but do not reliably surface in observable data.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by the ability to extract strategic dependence from deliberately noisy, information-concealed, and institutionally mediated behavior. Only strategic effects strong enough to overcome intentional randomization, private information, and market noise become empirically visible; finer strategic structure remains hidden.
2. Resolution (Spatial, Temporal, Spectral, Angular)
What “resolution” means in this field
In interaction-focused economics, resolution governs the ability to separate strategic components of multi-agent behavior—who is responding to whom, on what information, at what time, and through which mechanism.
Here, resolution is not physical but relational and temporal:
- Agent resolution: distinguishing individual strategic roles within a market.
- Action resolution: separating simultaneous or near-simultaneous moves.
- Information resolution: identifying what each agent knew at the moment of action.
- Strategic-channel resolution: separating price effects, quantity effects, signaling, and deterrence.
Resolution limits determine whether interaction appears structured and strategic or amorphous and market-level.
Sources of resolution limits
Resolution in interaction is constrained by:
- Simultaneity of actions: bids, trades, and responses occur within time windows finer than observation.
- Market clearing aggregation: individual strategies collapse into single prices or quantities.
- Matching opacity: who faced whom is often unobserved or anonymized.
- Private information: belief states and signals are hidden by design.
- Institutional batching: auctions, order books, clearing intervals, regulatory reporting lags.
- Observational coarsening: transactions recorded after execution, not during decision formation.
The resolution boundary
Below effective resolution:
- Strategic sequences appear simultaneous.
- Conditional responses cannot be temporally ordered.
- Individual influence collapses into aggregate outcomes.
- Signaling and noise become observationally indistinguishable.
- Coordination and coincidence cannot be separated.
Distinct strategic paths map to identical market outcomes.
Empirical manifestations of the limit
Resolution limits appear as:
- Observational equivalence among competing game forms.
- Inability to distinguish Stackelberg from Cournot behavior.
- Difficulty identifying first-mover or informational advantages.
- Collapsing of heterogeneous strategies into a single equilibrium.
- High sensitivity of results to assumed timing protocols.
In many cases, equilibrium is imposed because interaction cannot be resolved directly.
Consequences for inference
Because of resolution limits:
- Strategic timing is modeled rather than observed.
- Information sets are assumed, not measured.
- Mechanism identification is fragile.
- Fine-grained strategic dynamics are inferred indirectly.
- Empirical tests distinguish only broad classes of interaction.
Resolution sets the ceiling on strategic interpretability.
What lies beyond the limit
Below resolution lie:
- Micro-timing of belief updates.
- Conditional strategies with narrow triggers.
- Weak signaling effects embedded in noisy flows.
- Latent coordination not strong enough to shift aggregates.
These dynamics may exist but cannot be separated observationally.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by the field’s ability to resolve strategic relationships and timing within aggregated, simultaneous, and information-hidden environments. When strategic actions cannot be temporally or relationally separated, distinct interaction structures collapse into identical observed outcomes.
3. Dynamic Range and Saturation
What “dynamic range” means in this field
In interaction-focused economics, dynamic range governs the ability to observe both weak and strong strategic effects—small incentives, marginal signals, subtle deterrence—alongside dominant strategies, overwhelming market power, or binding institutional constraints.
The “detector” is the market or strategic environment itself: pricing rules, matching mechanisms, auction formats, regulatory thresholds, and payoff scales. Saturation occurs when interaction collapses into uniform outcomes or hard constraints that mask variation in strategic intensity.
Sources of dynamic-range limits
Dynamic range in interaction is constrained by:
- Market power extremes: monopoly or perfect competition compress strategic variation.
- Binding constraints: price floors/ceilings, capacity limits, margin requirements.
- Dominant strategies: equilibria where one action strictly dominates.
- Auction reserve prices and tick sizes: truncating bid dispersion.
- Institutional thresholds: compliance cutoffs, eligibility rules, reporting limits.
- Liquidity extremes: thin markets amplify noise; deep markets absorb signals.
These features bound how much strategic differentiation can be expressed.
The saturation boundary
At the low end of dynamic range:
- Weak strategic incentives fail to move prices or quantities.
- Subtle signaling is drowned out by routine market noise.
- Small belief differences produce identical observable actions.
At the high end:
- Prices, quantities, or strategies clip at institutional bounds.
- All agents converge on the same action.
- Strategic nuance disappears under dominant constraints.
In both regimes, interaction becomes observationally uninformative.
Empirical manifestations of the limit
Dynamic-range limits show up as:
- Price clustering at ticks, floors, or ceilings.
- Uniform bidding or pricing behavior.
- Inability to detect small strategic responses to policy changes.
- Structural breaks when constraints bind or relax.
- Apparent absence of strategic behavior in extreme regimes.
Observed interaction reflects bounds, not underlying strategy.
Consequences for inference
Because of dynamic-range limits:
- Strategic elasticities are identifiable only within mid-range regimes.
- Comparisons across market designs are scale-dependent.
- Policy evaluation is sensitive to whether constraints bind.
- Models extrapolate beyond observed ranges at high risk.
- “No effect” findings often reflect saturation, not neutrality.
Dynamic range determines where strategic behavior is visible at all.
What lies beyond the limit
Beyond observable dynamic range lie:
- Weak coordination and signaling effects.
- Strong but constrained strategies suppressed by rules.
- Latent market power in capped environments.
- Strategic heterogeneity masked by binding equilibria.
These forces may shape counterfactual outcomes but remain hidden in data.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by the finite dynamic range of market and institutional environments. When strategic incentives are too weak or too strong, interaction saturates into noise or uniformity, preventing empirical access to the full spectrum of strategic behavior.
4. Sampling Density, Coverage, and Missingness
What “sampling density and coverage” mean in this field
In interaction-focused economics, sampling density and coverage determine which strategic interactions, market participants, and relational structures are ever observed. Detection is constrained not by measurement precision, but by partial visibility of markets, matches, and sequences of interaction.
The “sample” consists of observed transactions, bids, prices, matches, contracts, or recorded strategic moves. Missingness arises whenever interactions occur off-record, off-platform, or outside observed pairings.
Sources of sampling limits
Sampling constraints in interaction arise from:
- Partial market visibility: only trades that clear or are reported are observed.
- Unobserved matches: who could have interacted but did not is invisible.
- Platform and venue fragmentation: parallel markets with incomplete linkage.
- Private negotiations: bilateral bargaining not recorded in public data.
- Network truncation: missing edges in interaction graphs.
- Regulatory or reporting thresholds: small or informal interactions excluded.
- Strategic concealment: deliberate avoidance of observable channels.
These omissions are systematic and often endogenous.
The coverage boundary
Below effective coverage:
- Counterfactual interactions cannot be evaluated.
- Strategic options appear constrained when they are not.
- Network effects are mismeasured or disappear.
- Power and influence are underestimated.
- Absence of interaction is misread as lack of incentive.
The unobserved interaction space silently shapes observed outcomes.
Empirical manifestations of the limit
Sampling limits appear as:
- Selection on observed trades or contracts.
- Biased estimates of competition and market power.
- Missing strategic responses to unobserved actions.
- Overestimation of equilibrium stability.
- Fragility of results to dataset expansion or linkage.
Observed interaction is a filtered projection of the true game.
Consequences for inference
Because of sampling limits:
- Strategic models are fit to incomplete games.
- Causal identification relies on strong exclusion assumptions.
- Collusion and coordination are hard to detect.
- Network-based inference underestimates connectivity.
- Policy conclusions depend on reporting scope.
Sampling defines which strategic worlds are empirically admissible.
What lies beyond the limit
Beyond coverage lie:
- Latent competitive threats.
- Shadow markets and informal bargaining.
- Suppressed entry and deterred interaction.
- Hidden coalitions and influence pathways.
- Strategic options never exercised but still constraining behavior.
These interactions shape equilibria without appearing in data.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by partial visibility of interactions and networks. Sparse, biased, or endogenous sampling creates structural blind spots in strategic analysis, rendering many potential interactions—and their effects—empirically inaccessible.
5. Channel Access, Penetration, and Occlusion
What “channel access” means in this field
In interaction-focused economics, channel access concerns whether the analyst can observe the strategic linkages themselves: who interacts with whom, what information is exchanged, what beliefs are formed, and which options are considered but not taken.
Here the “channel” is the interaction pathway—communication, observation, signaling, matching, negotiation—through which strategic dependence operates. Occlusion occurs when these pathways are private, indirect, fragmented, or deliberately concealed.
Sources of channel occlusion
Channel access in interaction is limited by:
- Private information: valuations, costs, beliefs, and signals known only to agents.
- Unobserved communication: informal talks, tacit signals, off-record coordination.
- Bilateral negotiation opacity: contracts and bargaining terms not publicly disclosed.
- Platform segmentation: parallel markets with incomplete visibility or linkage.
- Hidden network structure: missing edges, intermediaries, or influence pathways.
- Strategic concealment: deliberate obfuscation to avoid detection or imitation.
- Legal and reporting barriers: confidentiality, trade secrecy, data-protection rules.
These occlusions are often endogenous to strategic behavior.
The access boundary
Below effective channel access:
- Strategic intent cannot be directly observed.
- Information sets are inferred, not known.
- Absence of interaction is ambiguous (no incentive vs. deterrence).
- Observed outcomes collapse multiple unseen pathways.
- Influence and coordination operate without visible traces.
The interaction exists, but the observational route is blocked.
Empirical manifestations of the limit
Channel occlusion appears as:
- Reliance on reduced-form outcomes rather than mechanisms.
- Difficulty distinguishing competition from collusion.
- Inability to observe belief updates or expectation alignment.
- Weak tests of signaling and deterrence theories.
- Heavy dependence on institutional assumptions to reconstruct games.
Markets reveal results, not the full strategic circuitry.
Consequences for inference
Because of channel-access limits:
- Game structure is assumed rather than observed.
- Strategy attribution is fragile.
- Identification relies on exclusion restrictions or natural experiments.
- Network effects are underestimated or mischaracterized.
- Policy analysis risks misdiagnosing the operative mechanism.
Strategic analysis operates under partial observability by necessity.
What lies beyond the limit
Beyond accessible channels lie:
- Tacit coordination without explicit signals.
- Latent threats and deterrence.
- Informal coalitions and alliances.
- Private information cascades.
- Strategic options never exercised but constraining behavior.
These shape equilibria without entering the data.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by occlusion of the strategic channels themselves. Information exchange, coordination, and influence often occur through private or hidden pathways; where these channels are inaccessible, strategic structure must be inferred indirectly and remains only partially observable.
6. Confounding, Interference, and Identifiability
What “confounding and identifiability” mean in this field
In interaction-focused economics, this detection limit governs whether observed market or strategic outcomes can be uniquely attributed to a specific interaction mechanism—competition, collusion, signaling, learning, deterrence, or institutional design—rather than merely detected as an outcome consistent with many mechanisms.
Here the problem is acute: strategic environments are generative, and equilibrium behavior deliberately compresses multiple causal paths into the same observable result.
Sources of confounding and interference
Confounding in interaction arises from overlapping strategic mechanisms:
- Competition vs. collusion: similar price or quantity patterns can arise from both.
- Signaling vs. screening: observed actions may reflect sender signaling or receiver selection.
- Beliefs vs. payoffs: actions driven by expectations mimic payoff changes.
- Strategic substitution vs. complementarity: responses offset or reinforce each other in indistinguishable ways.
- Simultaneity: prices, quantities, and strategies determined jointly.
- Equilibrium multiplicity: different equilibria generate identical observables.
- Institutional effects vs. agent strategy: rules and behavior are observationally entangled.
These mechanisms interfere at the level of outcomes.
The identifiability boundary
Below effective identifiability:
- Distinct games rationalize the same data.
- Strategy profiles cannot be uniquely recovered.
- Belief structures are observationally hidden.
- Timing and causality collapse into simultaneity.
- Counterfactual predictions diverge despite identical fits.
The interaction is observed, but its strategic architecture is not.
Empirical manifestations of the limit
Identifiability limits appear as:
- Observational equivalence across competing market models.
- Heavy reliance on equilibrium selection assumptions.
- Sensitivity of conclusions to timing or information assumptions.
- Difficulty detecting tacit coordination.
- Structural parameters identified only within narrow model classes.
Empirical interaction analysis often tests classes of mechanisms, not specific ones.
Consequences for inference
Because of confounding and identifiability limits:
- Strategic intent cannot be directly inferred.
- Causal claims about mechanisms are fragile.
- Policy conclusions depend on assumed game form.
- Welfare and efficiency assessments vary by model.
- Reduced-form evidence dominates structural certainty.
Inference proceeds by exclusion, not direct confirmation.
What lies beyond the limit
Beyond identifiability lie:
- Exact belief hierarchies.
- Precise strategic contingencies.
- Latent coordination without overt signals.
- Unexercised but credible threats.
These shape outcomes while remaining empirically indistinguishable.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by confounding among strategic mechanisms. Multiple interaction structures—competition, collusion, signaling, learning—can generate identical observable outcomes, imposing identifiability limits that prevent unique causal attribution from interaction data alone.
7. Calibration Drift and Definition Instability
What “calibration drift and definition instability” mean in this field
In interaction-focused economics, this detection limit concerns whether observed interaction patterns remain comparable across time, markets, and institutional contexts. The issue is not whether prices, bids, or contracts are recorded correctly at a moment, but whether the same observed action represents the same strategic meaning as rules, platforms, and norms evolve.
Here, “calibration” includes market design, contract definitions, reporting standards, enforcement intensity, and strategic conventions. Drift occurs when these change, altering the mapping between strategy and observable outcome.
Sources of instability
Calibration drift and definition instability in interaction arise from:
- Market design changes: auction rules, tick sizes, matching algorithms.
- Regulatory evolution: disclosure rules, antitrust enforcement, reporting thresholds.
- Contract standardization shifts: new clauses, risk-sharing norms, indexation practices.
- Technological change: trading speed, information access, platform UX.
- Strategic norm evolution: learning, imitation, and convention formation.
- Data-definition changes: reclassification of transactions or instruments.
- Cross-market heterogeneity: identical actions carrying different meanings across venues.
These shifts are often incremental and endogenous.
The stability boundary
Below effective stability:
- The same price or bid no longer implies the same strategy.
- Observed coordination may reflect rule changes, not behavior.
- Strategic comparisons across time or markets become ambiguous.
- Apparent regime shifts may be measurement artifacts.
- Model parameters lose invariant interpretation.
Interaction remains observable, but its interpretive frame drifts.
Empirical manifestations of the limit
Instability appears as:
- Structural breaks aligned with rule changes.
- Parameter instability across samples.
- Sensitivity of strategic conclusions to institutional context.
- Difficulty pooling data across platforms or periods.
- Conflicting evidence about market competitiveness.
Observed interaction lacks a fixed semantic anchor.
Consequences for inference
Because of calibration and definition instability:
- Long-run studies conflate behavior change with institutional change.
- Cross-market comparisons require heavy contextual adjustment.
- Structural models must be re-specified repeatedly.
- Policy evaluation depends on institutional stability assumptions.
- Replication across time and venues is limited.
Strategic inference is locally coherent but globally fragile.
What lies beyond the limit
Beyond stable calibration lie:
- True evolution of strategic behavior.
- Robust comparison of market power over time.
- Long-run learning and norm formation.
- Generalizable mechanism design conclusions.
These goals exceed what drifting interaction data can securely support.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by calibration drift in market rules, institutions, and strategic conventions. Identical observed actions may encode different strategic meanings across time and venues, undermining stable inference unless institutional context is explicitly controlled.
8. Rarity and Statistical Power
What “rarity and statistical power” mean in this field
In interaction-focused economics, this detection limit concerns whether strategic events, equilibria, or interaction patterns occur often enough to be empirically distinguished from background variation. The issue is not whether strategic mechanisms exist, but whether they materialize with sufficient frequency, duration, or magnitude to be reliably detected in interaction data.
Here, rarity applies to events (e.g., crises, entry wars), strategies (e.g., predation, tacit collusion), and equilibria (e.g., coordination failures). Statistical power governs whether observed interaction outcomes can reject null or simpler strategic explanations.
Sources of rarity and low power
Rarity in interaction arises from several structural features:
- Infrequent strategic episodes: price wars, collusion breakdowns, deterrence tests.
- Rare equilibria: coordination failures or multiple equilibria realized only under narrow conditions.
- Tail market states: liquidity freezes, extreme volatility, capacity shortages.
- Low-frequency policy shocks: major rule changes or enforcement actions.
- Sparse matching: limited repetitions between the same agents.
- Short strategic windows: brief periods where incentives align for detection.
Even high-volume transaction data may contain few instances of the relevant strategic configuration.
The power boundary
Below effective statistical power:
- Strategic mechanisms blend into routine market noise.
- Rare equilibria cannot be empirically distinguished.
- Weak coordination or deterrence effects go undetected.
- Tail behaviors are misclassified as anomalies.
- Null findings reflect insufficient observation, not absence of strategy.
Observed interaction is biased toward common, stable regimes.
Empirical manifestations of the limit
Rarity and power limits appear as:
- Difficulty detecting tacit collusion without prolonged episodes.
- Inconclusive tests of predatory pricing or entry deterrence.
- Wide confidence intervals on strategic-response parameters.
- Conflicting empirical results across samples or periods.
- Heavy dependence on case studies or natural experiments.
Empirical interaction studies are often underpowered for rare strategic phenomena.
Consequences for inference
Because of rarity and power limits:
- Strategic conclusions emphasize average behavior.
- Tail risks and rare mechanisms are underrepresented.
- Policy evaluation underestimates low-probability harms.
- Structural models extrapolate from limited evidence.
- Absence of detected strategy is routinely misread as absence of strategy.
Inference favors frequency over consequence.
What lies beyond the limit
Beyond observable power lie:
- Rare coordination failures with large welfare effects.
- Latent collusion that collapses quickly.
- Strategic brinkmanship resolved before observation.
- Extreme market responses triggered only in tails.
These interactions shape outcomes despite sparse empirical traces.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by rarity of strategic events and insufficient statistical power. Many strategically important phenomena occur too infrequently or briefly to be reliably detected, so non-detection often reflects limited observation rather than absence of strategic structure.
9. Measurement Back-Action and Disturbance
What “measurement back-action” means in this field
In interaction-focused economics, measurement back-action occurs when monitoring, disclosure, enforcement, or data collection alters strategic behavior itself. Because agents anticipate observation and response, the act of measuring interaction reshapes incentives, strategies, and equilibria.
Here the “measurement” includes audits, reporting requirements, surveillance, transparency rules, experimental market observation, and public statistics. Disturbance arises because strategic agents react to being observed.
Sources of measurement disturbance
Back-action in interaction arises from structurally strategic responses:
- Strategic adaptation to monitoring: agents change tactics to avoid detection or scrutiny.
- Disclosure effects: transparency alters bargaining positions, prices, and coordination.
- Enforcement anticipation: behavior shifts in response to expected penalties or audits.
- Observer-induced signaling: actions are chosen to influence regulators, rivals, or audiences.
- Market design feedback: measurement rules become part of the game being played.
- Data-driven gaming: agents optimize against metrics rather than underlying objectives.
- Experimental interference: lab or field experiments change strategic timing and responses.
Measurement becomes a strategic input, not a neutral probe.
The disturbance boundary
Below effective non-disturbance:
- True strategic intent cannot be observed without alteration.
- Coordination and deterrence patterns shift under scrutiny.
- Equilibria selected under observation differ from unobserved ones.
- Strategic silence or avoidance replaces informative action.
- Observed interaction reflects compliance or signaling, not baseline strategy.
The signal exists, but strategic response to measurement dominates it.
Empirical manifestations of the limit
Back-action appears as:
- Regulatory arbitrage following new reporting rules.
- Price clustering or behavior changes around audit thresholds.
- Reduced collusion visibility under heightened monitoring.
- Shifts in timing or venue to evade observation.
- Divergence between measured and unmeasured markets.
Observed interaction adapts to the measurement regime.
Consequences for inference
Because of measurement back-action:
- Strategic behavior cannot be treated as measurement-invariant.
- Causal inference is confounded by anticipatory responses.
- Policy evaluations overstate or understate true effects.
- Structural models must incorporate monitoring as endogenous.
- External validity depends on the measurement environment.
Interaction data are inseparable from the observation regime.
What lies beyond the limit
Beyond non-disturbing measurement lie:
- Latent coordination absent scrutiny.
- Unobserved bargaining postures.
- Strategies viable only in low-visibility settings.
- Counterfactual equilibria without monitoring.
These strategic forms are reshaped or suppressed by observation.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by measurement back-action. Monitoring, disclosure, and enforcement alter incentives and equilibria, so observed interaction reflects strategic response to observation rather than an undisturbed strategic process, imposing intrinsic limits on what interaction data can reveal.
10. Computational and Algorithmic Tractability
What “computational tractability” means in this field
In interaction-focused economics, computational and algorithmic tractability limits whether strategic environments, equilibria, and belief hierarchies can be computed, estimated, or simulated within feasible resources. The constraint is not whether strategic structure exists, but whether it can be explicitly solved or recovered given the combinatorial complexity of multi-agent interaction.
Here the “instrument” is the algorithmic machinery for game solving, equilibrium computation, estimation of strategic models, network analysis, and simulation of interacting agents.
Sources of computational intractability
Tractability limits in interaction arise from structural features of strategic systems:
- Equilibrium computation hardness: multiple equilibria, mixed strategies, fixed-point problems.
- High-dimensional strategy spaces: many actions, contingencies, or states per agent.
- Belief hierarchies: beliefs about beliefs expand recursively.
- Simultaneity and feedback: joint determination of actions defeats sequential decomposition.
- Network-scale interaction: strategic dependence across large graphs.
- Dynamic games: state spaces explode over time.
- Endogenous information: signaling and learning alter the game as it is solved.
These limits persist even with complete observability of outcomes.
The tractability boundary
Below effective tractability:
- Full game forms cannot be enumerated or solved.
- Equilibrium selection cannot be computed reliably.
- Strategic parameters are weakly estimable at scale.
- Exact counterfactuals are infeasible.
- Models must collapse strategy spaces to remain solvable.
The interaction exists, but its strategic logic cannot be fully computed.
Empirical manifestations of the limit
Computational limits appear as:
- Restriction to simple game forms (e.g., Cournot, Bertrand).
- Use of reduced-form or partial-equilibrium models.
- Reliance on symmetry or representative-agent assumptions.
- Approximate equilibria or heuristic solution concepts.
- Sensitivity of estimates to algorithm choice and initialization.
Observed structure reflects computational feasibility as much as strategic reality.
Consequences for inference
Because of computational limits:
- Strategic richness is systematically under-modeled.
- Identification exists in theory but not in practice.
- Policy simulations are confined to simplified environments.
- Network and multi-agent effects are truncated.
- Competing strategic narratives persist without resolution.
Inference is bounded by what can be solved, not just what can be observed.
What lies beyond the limit
Beyond tractability lie:
- Large-scale strategic networks with heterogeneous agents.
- Deep belief hierarchies and signaling equilibria.
- Fully dynamic competitive and cooperative games.
- Exact recovery of strategic response functions.
These structures may govern outcomes but cannot be computed directly.
In Interaction (Markets, Strategy & Mechanisms), detection is limited by computational and algorithmic tractability. Strategic environments may be well-defined and empirically grounded, yet remain beyond feasible computation due to equilibrium complexity, dimensionality, and feedback, forcing analysis to rely on simplified or approximate representations of interaction.