Prisoner's Dilemma,
expanded.

Abstract

An extension of the classical Prisoner's Dilemma that introduces a fear-of-capture parameter among criminals who collaborate on illicit work. The payoff matrix is reshaped so that the dominant-strategy equilibrium can shift with enforcement pressure.

Method

Analytical game-theoretic derivation; simulated best-response dynamics to visualise equilibrium shifts.

The setup

Classical PD assumes fixed payoffs. In the real world, criminal collaborators face something the textbook ignores: the expected cost of being caught while en route between "cooperate" and "defect." We introduce a scalar φ — fear of capture — that scales the off-diagonal payoffs downward, and study how equilibria deform as φ moves.

Result

For φ above a threshold, the cooperate–cooperate cell becomes dominance-solvable — a result that is trivial in the original game but reappears with structure once fear is introduced. The threshold maps neatly to observable enforcement intensities.