At the level of Interaction, invariants specify what must remain fixed for a multi-agent system to be structurally coherent. While laws of interaction restrict which joint actions, strategies, and paths of play are admissible, invariants identify what those laws preserve across all admissible joint configurations, given the strategic interdependence of agents.
Interaction invariants do not concern individual preference coherence, nor do they summarize aggregate outcomes. They anchor compatibility across agents: whether strategy profiles can coexist, whether equilibria can persist, whether incentives remain aligned, and whether probabilistic mixtures remain well-formed. Variation is allowed—agents may differ, strategies may change, paths may unfold—but only insofar as these preserved structures remain intact.
Because interaction involves multiple decision-makers, invariants at this level are inherently relational. They constrain not what any one agent does in isolation, but what combinations of actions and responses can jointly exist without contradiction. Making these invariants explicit clarifies which strategic configurations are structurally admissible and which are ruled out regardless of beliefs, dynamics, or coordination mechanisms.
SAT – Structure – Invariants – Interaction (Markets, Strategy & Mechanisms)
| Invariant | What stays fixed | What variation must respect |
|---|---|---|
| Balance | Joint admissibility of strategy profiles | All agents’ strategies must be simultaneously feasible |
| Symmetry | Strategic structure under relabeling | Renaming players or equivalent strategies does not change the game |
| Stability | Equilibrium configuration | No unilateral deviation creates pressure to move away |
| Optimality | Incentive alignment / no profitable deviation | No agent can improve payoff given others’ actions |
| Distribution | Mixed-strategy probability structure | Randomized play respects probability coherence |
Taken together, the invariants of Interaction define the structural limits of coordination. They ensure that joint actions remain feasible, that equilibria are stable against deviation, that incentive structures do not undermine prescribed outcomes, and that stochastic strategies preserve coherent probability structure. Violations at this level do not indicate poor coordination or inefficiency; they indicate strategic incompatibility within the defined interaction framework.
These invariants are conditional by nature. Their force depends on clearly specified assumptions about strategy spaces, information, institutional rules, and admissible deviations. When those conditions hold, the invariants are absolute; when they fail, the interaction regime itself ceases to apply. This conditionality is a feature of strategic structure, not a weakness.
Interaction invariants therefore occupy the critical middle layer of economic structure. They connect internally coherent individual choices to system-level outcomes by determining which patterns of interdependence are possible at all. Only interactions that preserve these invariants can be meaningfully embedded in markets, mechanisms, or higher-level aggregate descriptions.