is(t)i_s(t) = short-term instrumental interest (e.g., profit, access)
il(t)i_l(t) = long-term relational or structural interest (e.g., market shaping, alliance durability)
(t)\theta(t) = agent's orientation toward ambiguity and transparency (meta-intent parameter)
These interest vectors shape how agents interpret zones, select strategies, and anticipate future configurations.
2. Strategic Zone Transition as a Relational Mechanism
Each relational zone (White, Green, Yellow, Red, Black, Clear) constitutes not only a state but also a strategy space with different rules of interaction. Transitions between these zones are not merely reactive but often strategically engineered by agents pursuing shifting constellations of interest.
Let Zi(t){W,G,Y,R,B,C}Z_i(t) \in \{W, G, Y, R, B, C\} represent the zone position of agent ii at time tt.
We define a zone transition function:
Zi(t+1)=f(Zi(t),Ii(t),Zj(t),Mij(t),(t))Z_i(t+1) = f\left(Z_i(t), I_i(t), Z_j(t), M_{ij}(t), \Psi(t) \right)
where:
Zj(t)Z_j(t): zone state of interaction partner or institutional counterpart
Mij(t)M_{ij}(t): memory matrix of past interaction outcomes between ii and jj
(t)\Psi(t): macro-structural context (e.g., shocks, institutional shifts, policy changes)
This framework moves beyond single-round or repeated-game logic by allowing agents to:
Intentionally induce ambiguity to create or delay transitions (e.g., using the Yellow Zone to stall conflict or extract concessions)
Sacrifice short-term interests to ascend toward the Clear Zone for long-term positioning
Engineer betrayals or fake cooperation as zone-manipulative tactics (e.g., simulate Green but act Black)
Such dynamics have no full analogue in classical equilibrium-based or static decision models.
3. Transition Cost and Strategic Friction
Zone changes are not costless. Each movement incurs transactional, emotional, reputational, or cognitive costs, formalized as:
