'The Prince' - A Robust Strategy in the Repeated Prisoner's Dilemma with Noise

Abstract

The Repeated Prisoner's Dilemma is a central model for the evolution of cooperation between selfish agents. The evolution of strategies in the Repeated Prisoner's Dilemma is examined using a computer simulation that uses a genetic algorithm to introduce new strategies. The simulation differs from prior simulations by modeling strategies as finite state automata of arbitrary length. This permits complex strategies which can be (relatively) easily analyzed.

A closely related class of strategies is found to be robust in a noisy environment. The strategy, called "The Prince" for its combination of fairness and ruthless opportunism, can be summarized by the following aphorisms:

Win-Stay, Lose-Shift • Never give a sucker an even break • If you can't beat 'em, join 'em

Punishment proportionate to the crime • Crime doesn't pay • Forgive a wrongdoer who has paid his debt

No strategy can be strictly stable, so the reign of the Prince eventually comes to an end. The simulation permits these transitions to be analyzed. A Prince that is lenient in its punishment, so that crime only just doesn't pay, will eventually be invaded directly when a critical mass of Hawk is able to exploit its leniency. A Prince that punishes more harshly will slowly be displaced by a more lenient rival that forgives accidental defections, before collapsing when the Prince declines to the point that Hawk is no longer kept in check.

Keywords: Evolutionary game theory, modeling morality, repeated prisoner's dilemma, genetic algortihm

JEL Classification: C72, C73, D70