Science Analysis Template
These are the structural patterns found across all Scientific Disciplines
This section evaluates whether the rules governing strategic and market interaction form a logically coherent system. Models of interaction layer strategic behavior, information structures, incentives, feasibility constraints, and equilibrium concepts on top of one another, often across multiple institutional or market settings. Consistency here requires that these layers jointly admit well-defined outcomes: strategies must be feasible under the rules, beliefs must align with information, incentives must not contradict resource constraints, and equilibrium concepts must match the assumed game structure. The purpose of this section is to verify that interaction models do not demand outcomes that their own rules make impossible, and that market- or mechanism-level conclusions genuinely follow from the underlying strategic architecture.
The 10 Universal Consistency Families
1) Definitional consistency
What it is:
The core primitives of interaction—such as agent, strategy, action, information, payoff, belief, market, mechanism, and equilibrium—are defined coherently and used consistently across strategic, market, and institutional analyses. In particular, the theory must be explicit about what counts as an interaction (strategic dependence among agents), how strategies are specified (pure vs. mixed, contingent on information or history), what information agents possess (complete, incomplete, asymmetric), and how payoffs are generated. If equilibrium concepts are used (e.g., Nash, subgame-perfect, Bayesian), their definitions must align with the assumed information structure and strategic space throughout the analysis.
Typical failure:
The analysis mixes incompatible strategic or informational definitions. Common failures include treating agents as price-takers in one part of a model and strategic price-setters in another without redefining the interaction; using payoff functions that implicitly assume complete information while later invoking beliefs or signaling; or switching between equilibrium concepts (e.g., Nash vs. dominant strategies) as if they were interchangeable. Another frequent error is conflating mechanisms (rules mapping actions and reports to outcomes) with markets (decentralized interaction processes), or assuming truthful reporting while also allowing incentives to misreport. These definitional slippages create contradictions about who interacts with whom, under what information, and according to which strategic rules.
2) Axiomatic / rule consistency
What it is:
The rule-set governing strategic interaction—game rules, timing, information structures, strategy spaces, belief-updating rules, and equilibrium requirements—contains no internal contradictions. The axioms defining how agents choose strategies, form beliefs, and respond to others’ actions must jointly support a coherent notion of strategic outcome. Incentive rules, feasibility constraints, and equilibrium conditions must be mutually satisfiable, so that the model does not permit deriving both that a strategy profile is an equilibrium and that it is not under the same assumptions.
Typical failure:
The analysis combines incompatible strategic rules or solution concepts. Common failures include assuming agents best-respond to beliefs while also allowing beliefs that violate Bayes’ rule; specifying a timing or information structure that makes certain strategies feasible while later ruling them out implicitly; or imposing incentive-compatibility, individual rationality, and feasibility constraints that cannot all be satisfied together. Another frequent error is switching between equilibrium concepts (e.g., Nash, subgame-perfect, Bayesian) without adjusting the underlying rules about information and timing, or layering mechanism-design constraints onto a model whose rules already preclude truthful or strategic reporting. In these cases, the axioms governing interaction negate one another, and the strategic system collapses into inconsistency rather than yielding a well-defined outcome.
3) Constraint compatibility
What it is:
All constraints governing strategic and market interaction—such as feasibility constraints, incentive constraints, information constraints, timing restrictions, and participation requirements—can be satisfied simultaneously. There must exist at least one configuration of strategies, beliefs, and outcomes that respects every stated rule of the interaction. This ensures the strategic or market model defines a non-empty feasible set of outcomes or equilibria.
Typical failure:
The model imposes mutually incompatible constraints. Common failures include requiring incentive compatibility, individual rationality, and feasibility in a mechanism where no allocation can satisfy all three; specifying market-clearing conditions while also imposing price controls or rationing rules that prevent clearing; or assuming strategic best responses under information structures that do not permit agents to form the required beliefs. Another frequent error is combining participation constraints with payoff or transfer rules that make every agent worse off than their outside option. In such cases, the interaction has no feasible equilibrium or outcome, because the constraints jointly demand an impossible configuration of strategies and allocations.
4) Conservation / accounting consistency
What it is:
Any conserved quantities or accounting identities embedded in an interaction—such as goods, money, transfers, probabilities, or surplus—are respected by the rules of trade, strategy, and mechanism design. The allocation rules, payoff functions, and transfer schemes must ensure that what leaves one agent or sector appears somewhere else in the system, and that totals implied by market-clearing or balance conditions are preserved as the interaction unfolds.
Typical failure:
The model allows resources, money, or surplus to be created or destroyed without an explicit source. Common failures include specifying market trades in which total expenditures exceed total receipts; defining payoff functions that double-count transfers or omit them for some agents; or constructing mechanisms where promised transfers exceed the available budget. Another frequent error is allowing probability mass to drift in strategic or stochastic interaction—such as mixed strategies or random matching processes whose probabilities do not sum to one. In these cases, the interaction’s “books” do not tally, and the strategic or market model violates basic accounting consistency.
5) Symmetry / invariance consistency
What it is:
If an interaction model assumes symmetry or invariance—such as identical agents, symmetric strategy spaces, anonymity in mechanisms, or invariance to relabeling of players, goods, or strategies—then all strategic predictions must respect those assumptions. Outcomes should not depend on arbitrary labels, ordering of players, or equivalent representations of strategies or markets. When a game or mechanism is symmetric by construction, equilibria and predicted payoffs must reflect that symmetry unless an explicit symmetry-breaking feature is introduced.
Typical failure:
The model produces outcomes that depend on labels or representations that should be irrelevant. Common failures include deriving asymmetric equilibria in a game with identical players and no asymmetry in payoffs, information, or timing; obtaining different results after permuting player identities or strategy labels; or designing a “neutral” mechanism whose outcomes depend on naming conventions or reporting formats. Another frequent error is assuming symmetric information or beliefs while introducing asymmetric strategic reasoning or tie-breaking rules that are not justified by the model. In such cases, the interaction violates its own invariance assumptions, signaling either a mathematical mistake or an implicit, unacknowledged symmetry-breaking rule.
6) Limit / correspondence (bridge) consistency
What it is:
When multiple models of interaction, markets, or mechanisms apply to overlapping regimes, they must agree in the domain where both are intended to hold. More general strategic frameworks should reduce to simpler ones under appropriate limits—for example, games with incomplete information reducing to complete-information games as uncertainty vanishes, or dynamic games reducing to static games when timing and history are irrelevant. Different formulations of the same interaction (analytical vs. numerical, reduced-form vs. structural) must yield compatible predictions in their common domain.
Typical failure:
A strategic or market model fails to reproduce standard results in the limit it claims to approximate. Common failures include Bayesian games that do not converge to Nash equilibria as information becomes common knowledge; mechanism-design models whose outcomes do not reduce to competitive market results when strategic power is removed; or dynamic interaction models that yield different equilibria than their static counterparts when adjustment frictions or intertemporal elements are set to zero. Another frequent error is aggregating or simplifying strategic interactions in ways that break feasibility or incentive properties in the limit. In these cases, the bridge between models collapses, indicating an inconsistency in how interaction is generalized or reduced.
7) Statistical / probabilistic consistency
What it is:
All probabilistic components of strategic and market interaction—such as mixed strategies, beliefs about types, random matching, noise in signals, or stochastic mechanisms—are internally coherent and follow a single, consistent probability framework. Probabilities must be properly normalized, belief-updating rules must align with how uncertainty is generated, and expected payoffs or outcomes must correspond to the underlying probability distributions assumed in the model.
Typical failure:
The model violates basic probabilistic coherence or mixes incompatible interpretations of uncertainty. Common failures include mixed strategies that do not sum to one; beliefs that are inconsistent with Bayes’ rule given the specified information structure; or payoff calculations that implicitly double-count or omit probabilistic events. Another frequent error is assuming independent random shocks while also introducing correlated information or common signals without adjusting the probability model. In such cases, the interaction’s probabilistic structure contradicts itself, undermining equilibrium predictions and strategic reasoning.
8) Operational / measurement consistency
What it is:
The theoretical objects used to describe interaction—such as strategies, beliefs, information sets, payoffs, market prices, and mechanism outcomes—are measured or inferred in ways that correspond to their definitions in the model. Observed actions, bids, prices, messages, or transactions must be valid operational proxies for the strategic variables the theory specifies. Empirical or experimental procedures used to identify strategies, beliefs, or equilibria must align with the assumed information structure and strategic rules.
Typical failure:
The measurement procedure captures something other than the theoretical construct. Common failures include inferring strategic beliefs from observed actions when multiple belief–strategy combinations are consistent with those actions; treating observed prices as equilibrium prices when markets are out of equilibrium or subject to frictions not modeled; or measuring incentives or payoffs using accounting data that do not reflect agents’ actual objective functions. Another frequent error is using experimental or institutional data generated under one set of rules to test a model that assumes a different timing, information structure, or mechanism. In these cases, the operational definition no longer matches the theoretical notion of interaction, creating inconsistency between the model and the evidence.
9) Cross-scale / multi-level consistency
What it is:
Descriptions of interaction at different levels—individual strategic behavior, pairwise or local interactions, and aggregate market or institutional outcomes—do not conflict with one another. Micro-level strategy choices and belief formation must be compatible with the macro-level properties attributed to markets or mechanisms, such as equilibrium prices, allocations, or institutional outcomes. When aggregate interaction patterns are invoked, there must be a coherent link showing how they arise from, or are at least consistent with, underlying strategic interactions.
Typical failure:
The model’s micro- and macro-level interaction descriptions imply incompatible outcomes. Common failures include specifying individual best-response behavior that, when aggregated, violates market-clearing or equilibrium conditions; assuming competitive market outcomes while modeling agents with strategic power that would prevent price-taking behavior; or deriving institutional or network-level stability from individual strategies that would actually destabilize those structures. Another frequent error is invoking “market-level” properties (efficiency, equilibrium, convergence) without mechanisms showing how decentralized strategic behavior produces them. In these cases, the higher-level interaction story demands results that the lower-level strategic rules cannot support, creating a cross-scale inconsistency.
10) Numerical / discretization consistency
What it is:
When computational or numerical methods are used to analyze strategic interaction, markets, or mechanisms—such as discretizing strategy spaces, approximating equilibrium conditions, or simulating market dynamics—the numerical scheme must preserve the core constraints and properties of the theoretical model. Incentive compatibility, feasibility, probability normalization, and symmetry conditions must not be violated by discretization or algorithmic choices. As numerical resolution increases, computed equilibria or outcomes should converge toward the predictions of the underlying interaction theory.
Typical failure:
The numerical implementation introduces artifacts that contradict the strategic model. Common failures include discretized strategy spaces that remove or create equilibria that do not exist in the continuous model; simulated mixed strategies whose probabilities do not sum to one; or market simulations that violate clearing or budget constraints due to rounding or truncation error. Another frequent error is using solution algorithms that implicitly break symmetry or impose tie-breaking rules not present in the theory, yielding spurious asymmetric outcomes. In these cases, the numerical results reflect discretization error rather than genuine strategic or market behavior.