Scale in Interaction identifies the level of granularity at which strategic interdependence becomes meaningful. This domain sits between the solitary agent of Choice and the system-level dynamics of Aggregation, requiring a scale that captures how agents influence one another through markets, institutions, contracts, and rules. If the scale is drawn too narrowly, strategic structure collapses; drawn too broadly, system-level forces overshadow the very interdependence that defines the domain.

A clearly defined scale ensures that equilibrium concepts, incentive structures, and information flows are applied at the resolution where cross-agent influence is the dominant driver of outcomes. It protects the analytical boundary of the domain by preventing micro-level choices or macro-level movements from being mistaken for strategic behavior.
The Scale Framework provides the formal apparatus for expressing these distinctions rigorously.

THE SCALE FRAMEWORK

1. Ontological Scale (What exists at this level of analysis?)

At the ontological scale of Interaction, the meaningful units are multiple decision-making agents whose choices influence one another. These agents are not merely co-present; they are mutually relevant. Each one’s feasible actions, outcomes, expectations, and opportunities are shaped by the presence and behavior of the others.

The environment also exists at this scale, but not as a passive backdrop. It includes rules, institutions, mechanisms, markets, or protocols that structure how agents affect one another. These structures are part of the ontology because they determine how interdependence is expressed—through prices, payoffs, signals, allocations, or informational channels.

The ontology of Interaction therefore contains:

many agents, each with independent decision-making capacity
patterns of influence, by which one agent’s actions alter another’s situation
institutional or rule-based structures that govern how influence is transmitted
shared environments, whose relevant features emerge from or depend on inter-agent relations

At this scale, no single agent defines the world; the world is jointly constituted by the set of agents and the system of relations connecting them.

This is a multi-entity world where interdependence is the fundamental fact of existence.

2. Resolution of Representation (How finely or coarsely are things described?)

In the domain of Interaction, the representation must be fine enough to capture how agents influence each other, yet coarse enough to avoid importing system-level forces that belong to Aggregation or internal psychological details that belong to Choice. The focus is on relational structure—how each agent’s actions, information, rules, or constraints shape the choices and outcomes of others.

The model explicitly represents:

multiple agents, each with their own feasible actions
the influence structure, specifying how one agent’s choices affect another’s opportunities or outcomes
rules or institutions, which determine how interactions occur (markets, games, contracts, protocols, mechanisms)
informational relationships, including who knows what and how beliefs are formed
equilibrium conditions, ensuring that agents’ choices are mutually consistent

Details that do not belong at this scale are abstracted away:

the internal psychological decomposition of each agent (belongs to Choice)
the evolution of system-wide states, aggregates, or long-run trajectories (belongs to Aggregation)
individual idiosyncrasies that do not affect strategic relations
fine-grained microdynamics that do not influence interdependence

The correct resolution must reveal:

who can influence whom,
what actions are available,
what information flows,
what rules govern interaction,
and what consistency conditions define the outcome.

Too fine a resolution introduces irrelevant detail and masks the structure of interdependence.
Too coarse a resolution erases strategic nuance, causing interactions to collapse into aggregates where the logic of the domain no longer applies.

The proper resolution for this domain is therefore:

sharp enough to represent strategic relationships and institutional structures
blurred enough to exclude system-level dynamics and individual psychological depth

This is the resolution at which Interaction becomes intelligible and analytically stable.

3. Temporal Scale (Over what timeframe do processes unfold?)

In the domain of Interaction, temporal scale determines the horizon over which agents influence one another and adjust their behavior in response to others. Time is no longer internal to a single decision-maker; it becomes the medium through which strategic relationships unfold. The appropriate temporal resolution must capture how actions, expectations, information, and responses propagate across agents.

Depending on the interaction structure, time may take several forms:

Single-shot interactions, where all decisions occur in one moment (e.g., sealed-bid auctions).
Sequential interactions, where agents act in turns and later choices depend on earlier ones.
Repeated interactions, where patterns, punishments, norms, or cooperation emerge over time.
Dynamic or evolving interactions, where agents update beliefs, adjust strategies, or respond to changing environments under stable rules.

The temporal scale must exclude:

the instantaneous isolated choice logic of a single agent (Choice), and
the long-run evolution of system-level variables and macro adjustments (Aggregation & Dynamics).

Within Interaction, temporal scale determines:

what counts as relevant change (shifts in strategies, expectations, or available actions),
which adjustments must be explicitly modeled (belief updating, learning, adaptation),
which can be treated as immediate,
and how causal influence moves across agents over time.

If the temporal resolution is too fine, irrelevant micro-events obscure the strategic structure.
If too coarse, strategic patterns—coordination, conflict, equilibrium refinement—collapse into aggregates that no longer reflect interdependence.

The correct temporal scale for Interaction is therefore:

broad enough to allow the unfolding of influence, response, and adaptation among agents,
narrow enough to remain centered on strategic behavior rather than system-level evolution,
and precise enough to capture the timing of interactions that define equilibrium.

This is the speed at which reality moves in a multi-agent world.

4. Interpretive Constraints (What conclusions are allowed at this scale?)

At the scale of Interaction, valid inferences must arise from relationships among multiple agents—how their actions, information, expectations, and constraints shape one another’s outcomes. Because this domain is defined by interdependence, conclusions must be grounded in cross-agent influence. Any inference that relies on solitary optimization (Choice) or on system-level evolution (Aggregation & Dynamics) lies outside this scale.

Permitted conclusions include statements about:

how one agent’s action alters another’s opportunities, payoffs, or beliefs
how rules or institutions structure the interaction among agents
how information asymmetries or signals affect behavior and outcomes
how equilibrium arises from mutually consistent choices
how coordination, conflict, competition, or cooperation emerge from interdependence
how agents adapt or respond to one another over time without invoking system-level forces

Forbidden conclusions include statements that imply:

outcomes determined solely by one agent’s internal decision process (Choice)
macro-state variables governing results rather than agent-to-agent influence (Aggregation)
system-wide propagation or adjustment dynamics
aggregate trajectories or long-run state evolution
conclusions derived from treating populations, distributions, or representative functions as primary objects
causal stories that rely on system structure rather than relational structure

These constraints exist to preserve the integrity of Interaction as the domain of strategic and institutional interdependence.
At this scale:

no inference can ignore the presence of multiple agents, because interdependence defines the ontology
no inference may rely on system-level state evolution, because those forces belong to Aggregation
no inference may collapse interaction into solitary decision-making, because Choice excludes relational structure

Violating these constraints produces classic category errors:

importing macro dynamics into a strategic model,
treating equilibrium as if it were a system trajectory,
or explaining cross-agent influence using one-agent logic.

The interpretive rule is precise:

Only conclusions derived from cross-agent influence, structured interaction, and relational consistency are valid at this scale.

Everything else belongs to another domain.

5. Canonical Scale Statement

The domain of Interaction operates at the scale of multiple decision-making agents whose choices, information, and constraints shape one another’s outcomes. At this level, representation focuses on the relational structure among agents—how actions influence others, how institutions and rules govern those influences, and how equilibrium arises from mutual consistency. Time is modeled as the horizon over which strategic adjustments, responses, and belief updates occur, but without invoking the evolution of system-level state variables. Valid inferences are limited to conclusions that emerge from cross-agent influence and the structures that mediate it, excluding any reasoning that relies on solitary optimization or on macro-level dynamics. This scale is the lawful operating level of Interaction: a multi-agent world defined by interdependence, strategic relevance, and the rules that shape their coordination.

Science Analysis Template

These are the structural patterns found across all Scientific Disciplines

1. Interaction occupies its own rung on the social-science scale ladder.

Across disciplines, each field sits on a defined rung of a size–organization ladder.
In the social sciences, that ladder runs:

individual → multi-agent group → organization → community → state → global system

Choice occupies the individual rung.
Aggregation & Dynamics occupies the system rung.

Interaction occupies the band directly above the individual and below the system:
the level where multiple agents coexist and exert influence over one another within a shared structure of rules, incentives, and information.

At this scale:

agents are distinct decision-making units,
their opportunities and outcomes depend on each other,
relational structure (who affects whom) becomes an object of study,
institutions and rules are part of the ontology.

Interaction is the first rung where interdependence exists as a real analytical force.

2. Scale transitions define the handoffs into and out of Interaction.

Just as physics hands off from quantum → classical at the emergence of large-scale coherence, Interaction hands off precisely at two points:

Downward (Transition to Choice):

If the analysis can be represented using only one agent’s preferences, constraints, and feasible actions—with no consequences determined by other decision-makers—then the problem is below the Interaction scale and belongs to Choice.

Upward (Transition to Aggregation & Dynamics):

If outcomes depend primarily on macro-state variables, system equilibria, propagation mechanisms, or aggregate effects, the scale has moved above Interaction.
At that point, strategic dependence is no longer the dominant determinant of behavior, and the model must transition to Aggregation & Dynamics.

Lateral (Transition to Institutional or Organizational Analysis):

If the system requires modeling of internal hierarchies, governance structures, or multi-layer organizational dynamics, the problem may move laterally into organizational theory or political science, depending on the nature of the structure.

These transitions are scale boundaries.
They prevent the dilution of Interaction with either micro-level individualism or macro-level system dynamics.

3. Interaction’s time scale must match the tempo of influence and strategic adjustment.

The master template treats time scale with the same precision as size scale.
For Interaction, the relevant temporal windows are defined by how long it takes influence to propagate across agents.

This includes:

Instantaneous or single-shot interactions (e.g., a sealed-bid auction).
Sequential timing (turn-taking, observing others before acting).
Repeated interactions (cooperation, retaliation, equilibrium refinement).
Dynamic games where belief updating, learning, or adaptation occurs over time.

What does not belong:

moment-scale internal processing (Choice),
long-run system-scale trajectories (Aggregation).

Thus the temporal window of Interaction is the time it takes for:

information to travel,
strategies to adjust,
expectations to update,
and institutions to coordinate behavior.

Too fine a temporal resolution collapses into psychology.
Too coarse collapses into macro-level system change.

Interaction’s time scale is the strategic horizon.

4. Interaction uses formal tools that are scale-independent but anchored to a multi-agent structure.

Formal sciences are scale-independent, but their application requires appropriate anchoring.
In Interaction, mathematical tools such as:

equilibrium concepts,
fixed point theorems,
mechanism design constraints,
game-theoretic solution concepts,
information-theoretic mappings,

are anchored to a representation in which multiple agents are simultaneously relevant.

These tools are invalid if:

the model collapses to a single agent (Choice),
the model shifts to macro-state variables and system equations (Aggregation),
the analysis requires biological, psychological, or computational sub-components of agents.

The domain remains legitimate only when the math maps to:

strategy sets,
information sets,
incentive constraints,
and relational payoff structures.

This maintains the structural identity of Interaction as the domain of multi-agent reasoning, not individual optimization or system dynamics.

5. Interaction is distinguished by its organizational level: relational, not individual or systemic.

In biology, organization follows:

molecule → cell → tissue → organ → organism → population → ecosystem → biosphere.

In social science, the parallel ladder is:

individual → interacting agents → organizations → institutions → polities → global systems.

Interaction occupies the second rung:

larger than an individual,
smaller than an organization,
defined by the links between decision-makers.