In Interaction, properties describe the attributes of multiple agents, their connections, and the institutions or rules governing their relationships. Because outcomes in this domain arise from interdependence, properties must capture the characteristics that shape how agents influence one another. These include action sets, information sets, payoff structures, beliefs, and the institutional constraints that mediate interaction.
Properties in Interaction determine how agents respond to one another, how incentives form, how coordination or conflict emerges, and how equilibrium is defined. They transform ontology (what exists) into usable analytical structure (how those things behave). Without precise properties—who knows what, who can do what, what the rules permit—there is no way to model strategic dependence or relational causation. Identifying these properties explicitly ensures that the domain remains centered on inter-agent influence rather than collapsing into individual decision-making (Choice) or system-level behavior (Aggregation).
Science Analysis Template
These are the structural patterns found across all Scientific Disciplines
This table lays out every property relevant to the Interaction domain, sorted into the seven universal property categories. Each row identifies a property that matters when multiple agents influence one another. It defines the property, explains how it functions in strategic or rule-based environments, shows how it is represented formally, and states why it belongs at this scale. Magnitude, Structure, Dynamics, Constraint, Information, and Evaluation now refer to inter-agent characteristics rather than internal, single-agent features. The Interaction category is populated here—the heart of this domain—because cross-agent influence, incentives, and institutional mediation shape all outcomes. No system-level or aggregate properties appear because those belong to Aggregation.
This table is the complete property set for multi-agent interaction.
- Magnitude → “How much?”
- Structure → “How arranged?”
- Dynamics → “How does it change?”
- Interaction → “What influences what?”
- Constraint → “What is allowed?”
- Information → “What is known or encoded?”
- Evaluation → “What is better or worse?”
| Property Category | Property | Definition / Meaning | Functional Role in Choice | How It Is Measured or Represented | Ontological Status (why it belongs) |
|---|---|---|---|---|---|
| Magnitude | Payoff magnitude | Numerical outcome each agent receives for joint actions | Allows agents to compare strategies; drives equilibrium | Payoff vectors, utility numbers | Core quantity agents respond to in interdependence |
| Magnitude | Action intensity / effort level | Quantitative measure of how strongly an agent takes an action | Affects others’ outcomes and best responses | Scalars or action levels | Matters only because it influences other agents |
| Magnitude | Transfer/payment size | How large any transfers, prices, or penalties are | Shapes incentives and feasible contracts | Payment functions, transfers | Exists because agents exchange value strategically |
| Structure | Influence structure | Pattern of which agents affect which others | Defines who responds to whom; shapes equilibrium form | Directed graphs, adjacency matrices | Foundational relational structure of the domain |
| Structure | Information structure | Who observes what and when | Determines beliefs, signaling, and strategic inference | Information partitions, signaling graphs | Essential pattern of strategic asymmetry |
| Structure | Institutional/Rule architecture | The rules mapping actions to outcomes | Shapes incentives, constraints, and feasible strategies | Mechanism design mappings, market rules | Formal backbone of interaction settings |
| Dynamics | Belief updating rule | How agents revise beliefs based on others’ actions | Drives strategy adjustment over time | Bayesian updating, learning rules | Dynamic property only meaningful with >1 agent |
| Dynamics | Strategic adjustment speed | How quickly agents respond to others | Determines convergence, cycles, and equilibria | Update functions, iterative best response | Exists only in a multi-agent world |
| Dynamics | Path dependence of interactions | How previous moves affect current possibilities | Enables reputation, punishment, cooperation | State variables over histories | Dynamic property arising from repeated interaction |
| Interaction | Strategic dependence | How one agent’s action changes another’s payoffs | The essence of the domain; defines incentives | Payoff interdependencies | Core defining property of Interaction |
| Interaction | Complementarity / substitutability | Whether actions reinforce or counteract each other | Determines multiple equilibria, coordination, competition | Cross-partial derivatives, payoff curvature | Governs how strategies relate |
| Interaction | Externalities | Unpriced spillovers between agents | Affects welfare, incentives, mechanism design | Off-diagonal effects in payoff matrices | Inter-agent influence not mediated by rules |
| Interaction | Communication channels | How agents send/receive signals | Enables signaling, cheap talk, persuasion | Message spaces, signaling games | Defines non-action pathways of influence |
| Constraint | Feasible action sets (multi-agent) | What each agent is allowed to do | Shapes strategic possibilities | Strategy sets, feasible strategy profiles | Multi-agent version of constraints |
| Constraint | Institutional constraints | Rules that limit possible outcomes or strategies | Prevents undesired behavior; shapes equilibria | Mechanism constraints, legal rules | Constraints exist at collective level |
| Constraint | Participation constraints | Conditions required for agents to join/accept | Limits mechanism viability | Individual rationality constraints | Only meaningful with multiple agents |
| Information | Beliefs about other agents | Probabilistic expectations about others’ choices | Central to equilibrium refinement and strategy | Belief hierarchies, priors | Fundamental epistemic property of interaction |
| Information | Information asymmetry | Differences in what agents know | Core driver of adverse selection, signaling, screening | Asymmetric information sets | Defines informational environment |
| Information | Uncertainty about rules or types | Not knowing others’ preferences, types, or constraints | Drives Bayesian games and mechanism design | Type spaces, distribution over types | Allows higher-order uncertainty |
| Evaluation | Payoff evaluation | How each agent ranks outcomes of joint actions | Shapes strategic preferences | Utility vectors, ordinal/comparative rankings | Evaluation extended to outcomes shaped by others |
| Evaluation | Strategic value of information | How much an agent values knowing something | Changes incentives to hide, reveal, or distort info | Value of information metrics | Evaluation in relational environment |
| Evaluation | Welfare comparisons across agents | Normative ranking of multi-agent outcomes | Enables mechanism evaluation, social choice | Social welfare functions | Only appears when >1 agent exists |