← T. Ryan Johnson

Exploring Spies in a Barrel

Move the parameters of the two-tier game of secrets and watch tolerated espionage, Open Secrets and the Executives' payoffs respond. Each Executive detects the rival Officer's operation with probability equal to its effort and chooses Reel In or Let Swim.

bin Oslan, Afiq, and T. Ryan Johnson. 2026. “Spies in a barrel: When to reel in espionage.” Journal of Theoretical Politics 38 (2): 87–109. doi:10.1177/09516298251403415

Open Secrets holds

Officer A's tolerated effort—set by Executive B
Officer B's tolerated effort—set by Executive A
Executive A's payoff—stage game: −1
Executive B's payoff—stage game: −1

Officer by Officer

Officer A, spying in BOfficer B, spying in A

Tolerated effort as patience rises

Each Officer's tolerated effort against its restraint bar under the chosen game. Open Secrets holds over the shaded stretch of δ.

Officer A's tolerated effortOfficer B'sOfficer A's barOfficer B's barOpen Secrets

Where Open Secrets holds

Symmetric states under the chosen game and its current parameter, mapped over α and δ. The dashed lines bound the base game's wedge, α ≤ δ ≤ α/(1−α).

Open Secretsfull effort let swimbase wedgecurrent (α, δ)

Patience thresholds

Formulas in use

Reading the result