Prisoner's dilemma and the free operant: John Nash, I'd like you to meet Fred Skinner.

Abstract

In separate chambers, responding by two pairs of pigeons was reinforced under concurrent random-ratio schedules of reinforcement. For each pair, the birds' schedules were coupled in such a manner that left- and right-key reinforcement probabilities were determined by the key being pecked by the other pigeon of the pair. In this way, a reinforcement matrix, like that of the popular Prisoner's Dilemma game of game theory, was created. The responding of all subjects soon gravitated to the choice combination identified by the mathematician John Nash as the equilibrium of the Prisoner's Dilemma game. This was found both before and after reversal of contingencies on the keys. In a second experiment, with a single pair of pigeons, stimuli signaling the choice of the paired pigeon had little lasting effect: responding again gravitated to the game's equilibrium. The results affirm earlier findings, demonstrating that Skinner's principle of positive reinforcement, together with Nashian mathematics, entirely accounts for iterative game-theoretic behavior. They extend these findings to the so-called free operant: to schedules of reinforcement in which responding is not constrained by stimulus-response sequencing (i.e., a trials procedure). The coupled schedule of reinforcement introduced here offers significant promise for the experimental analysis of economic and social behaviors.