Dilemma of the Boundary
One version of the Paradox of the Boundary is: which country owns the border? Attempts to impose a binary solution on this inherently non-binary problem have proven to be expensive and ineffective.
The topological paradox of the boundary translates to a game-theoretical dilemma. For each country must make this choice: shall we attempt to take the boundary, or not? If neither does, then there is peace, and both share the boundary. If both do, then there is war, and the boundary becomes no-man’s-land; and if only one does, then the aggressor wins.
The boundary can be advancing, retreating, deadlocked, or porous, in a prisoner’s-dilemma context. The boundary is negotiated.