A model of money counterfeits

This note offers a game-theoretic analysis of the strategic interaction between a central bank and a counterfeiter. Counterfeit notes cause a potential loss for consumers because such notes are confiscated when detected. The central bank is assumed to choose a bank note design that minimizes the sum of the production cost of the notes and of the expected loss to the non-counterfeiting part of the population. The counterfeiter maximizes his expected return. I find that this game has a pure strategy subgame perfect equilibrium, and this equilibrium is typically unique. Depending on parameter values (specifically on the face values of notes), there is either no counterfeiting or much counterfeiting in equilibrium. Intermediate cases are never an equilibrium.