notation.md

Notation

Basic Objects

• Gcal: space of possible games
• g: a specific game
• A(g): set of admissible actions in game g
• pi: policy
• pi_local: locally optimal policy
• pi_alt: feasible alternative policy

State and Dynamics

• x_t: aggregate state at time t
• o_t: future optionality
• l_t: lock-in
• z_t: remaining state variables
• F: state dynamics
• Phi: permanence or game-change dynamics

Payoffs and Value

• r(x, a, g): local payoff
• U(x_t, a_t, g_t): instantaneous structural utility
• J^pi(x_0, g_0): discounted structural value of policy pi
• delta: intertemporal discount factor
• lambda: optionality weight
• mu: lock-in weight
• c: generic cost
• chi: explicit exit or reconfiguration cost
• eta: weight of the explicit exit cost in the structural functional

Minimal Model

• exploit: local-gain-maximizing policy
• preserve: structurally prudent policy
• kappa_E: optionality survival factor under exploit
• kappa_P: closing factor for the gap to full optionality under preserve
• Delta r = r_exploit - r_preserve
• Gamma: structural optionality premium
• lambda_*: critical threshold for structural weight

Capture

• p_stay(r): probability of remaining in the game given observed payoff
• alpha, beta, gamma: parameters of the logistic permanence function
• e: perceived exit cost
• q: proxy for local competence
• tau_bad: time spent in the bad game