Axioms of Abstract Perfect-Information Strategy Games
An Abstract Perfect-Information Strategy Game is a finite, deterministic, turn-based system in which all game-relevant information is visible to all players at all times, and in which outcomes depend solely on player decisions.
Termination & Inevitability
Forced Termination
If a player is in a losing position, the game must eventually reach a terminal state against that player's will.
Bounded State Space
The total number of distinct game states reachable from the initial state is finite.
Non-Abusive Draws
A player may not force a draw solely by avoiding interaction while in a losing position.
Information & Determinism
Complete Observability
All game-relevant state is visible, explicit, and unambiguous to all players at all times.
Deterministic State Transition
Given a game state and a legal action, the resulting game state is uniquely determined.
State Sufficiency
Legality of actions and game outcomes depend only on the current game state, not on how it was reached.
Decision Structure
Non-Degenerate Choice
From non-terminal states, players must have more than one legal action available.
Strategic Non-Dominance
No single strategy or heuristic guarantees victory against optimal opposition.
Outcome Sensitivity
Differences in player decisions must be capable of producing different outcomes.
Structural Balance
Initial Positional Symmetry
The initial game state must not structurally privilege one player over another.
Contextual Power
Positional advantage must arise from interaction within the game state, not from static location alone.
Progression & Resolution
Irreversibility
Some player actions must have permanent effects on the game state.
Strategic Compression
As the game progresses, the space of reachable non-terminal states must decrease.
Formal Coherence
Rule Closure
All game rules must operate solely on the defined game state and its legal transformations.
Conceptual Coherence
All mechanics must be mutually consistent within a single, unified strategic framework.