At the level of Interaction, mechanisms specify the causal processes by which multiple decision-makers produce jointly admissible outcomes under strategic interdependence. While laws of interaction define which configurations of strategies and outcomes are permissible, and invariants specify what must remain fixed across admissible configurations, interaction mechanisms describe how agents’ actions are procedurally adjusted, filtered, and coordinated within those constraints.
Interaction mechanisms operate over multiple entities simultaneously. They transform individual action choices, information states, and institutional rules into joint strategy profiles or paths of play. These mechanisms do not assert equilibrium or incentive compatibility as requirements; rather, they describe the processes through which equilibria may be generated, selected, or maintained, and through which incompatible configurations are eliminated.
By isolating interaction mechanisms, the template separates strategic constraints from strategic production. This prevents equilibrium concepts, feasibility conditions, and impossibility results from being conflated with the causal processes that give rise to observable strategic outcomes.
SAT – Structure – Mechanisms – Interaction (Markets, Strategy & Mechanisms)
| Mechanism | Definition | Entities | Properties | Variables | Laws / Relations | Invariants Preserved | Conditions |
|---|---|---|---|---|---|---|---|
| Best-Response Adjustment | Procedural updating of agents’ admissible actions in response to others’ actions. | Agents | Payoff relations; admissible actions | Action choices | Mutual Best Response (Nash Equilibrium) | Stability; Optimality | Defined strategy sets and payoff functions |
| Strategic Compatibility Filtering | Removal of joint strategy profiles that violate joint feasibility or internal consistency. | Agents; strategy profiles | Joint admissibility; consistency | Admissible profiles | Joint Strategy Feasibility | Balance | Well-defined game form and rules |
| Incentive Alignment | Procedural shaping of outcome mappings so admissible actions coincide with agents’ incentives. | Agents; outcome rules | Incentive compatibility | Action–outcome mapping | Incentive Compatibility | Optimality | Institutional or mechanism rules |
| Equilibrium Realization | Procedural generation or selection of mutually admissible strategy profiles. | Agents; strategies | Mutual consistency | Equilibrium states | Nash Equilibrium; Equilibrium Existence | Stability | Compact strategy space; admissible selection process |
| Information Conditioning | Restriction of admissible strategies based on agents’ available information states. | Agents; information states | Information availability | Strategy contingencies | Strategic Consistency | Stability | Defined information structure |
| Randomized Strategy Mixing | Generation of admissible outcomes via probability-weighted strategy selection. | Agents; mixed strategies | Probability coherence | Strategy distributions | Mixed Strategy Validity | Distribution | Statistical independence |
Taken together, the mechanisms of Interaction define the procedural core of strategic systems. They account for action adjustment in response to others, filtering of inadmissible joint strategies, alignment of incentives with admissible outcomes, generation of equilibrium profiles, conditioning on information, and probabilistic mixing of strategies. Each mechanism produces admissible joint outcomes while preserving the invariants required by interaction theory.
These mechanisms do not explain preference formation, nor do they aggregate behavior into system-level quantities. Their role is intermediate and relational: to specify how individually coherent choices are transformed into strategically compatible configurations. When interaction mechanisms fail to operate, the result is not inefficiency or instability, but strategic incoherence within the defined game structure.
Interaction mechanisms therefore serve as the necessary bridge between individual choice processes and aggregate economic descriptions. Only once these mechanisms are explicit can aggregate mechanisms operate without importing hidden assumptions about coordination, equilibrium, or optimization.