Strategic Games & Temporal Logic

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Abstractions about adversarial strategy, combinatorial game values, temporal logic, coordinated protocols, index policies, and quantum games.

8 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Algebraic notation (chess) — Encode chess moves through destination-square coordinates plus compact symbols for pieces, captures, disambiguation, promotion, castling, check, and result under a shared rule set.
• Alternating-time temporal logic — A branching-time logic for concurrent games whose coalition modalities assert that selected agents have a strategy to ensure a temporal objective regardless of the other agents' choices.
• Gittins index — Assign each state of an eligible discounted Markov reward arm the greatest reward rate attainable before an adapted stopping time, enabling an optimal classical bandit policy by selecting the arm with largest current index.
• Lockstep protocol — A peer-to-peer multiplayer synchronization protocol that commits participants to concealed actions before revealing them, preventing one client from choosing after seeing another’s same-turn move.
• Nimber — Assign an impartial normal-play game position the unique Nim-heap value determined recursively by the minimum excluded values of its options and composed by nim-sum.
• Promoting adversaries — A mutually reinforcing rivalry in which opposing organizations gain attention, legitimacy or resources by attacking one another while avoiding decisive defeat.
• Quantum Game Theory — A strategic-interaction framework in which admissible strategies are quantum operations or measurements on specified quantum systems, with measurement-induced outcome probabilities and payoffs compared against a protocol-matched classical strategy set.
• Strategy-stealing argument — A nonconstructive game-theoretic proof that a second-player winning strategy would let the first player make a harmless opening move and then adopt that strategy, producing a contradiction.