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.

中文翻译：

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囚徒困境和自由操作员：约翰·纳什，我想让你认识一下弗雷德·斯金纳

在不同的房间中，两对鸽子的反应在并发随机比率强化计划下得到强化。对于每一对，鸽子的日程安排以这样的方式耦合：左键和右键强化概率由该对中的另一只鸽子啄的钥匙决定。这样，就创建了一个强化矩阵，就像博弈论中流行的囚徒困境博弈一样。所有受试者的反应很快就倾向于由数学家约翰·纳什确定的囚徒困境博弈均衡的选择组合。在按键意外事件逆转之前和之后都发现了这一点。在第二个实验中，只有一对鸽子，表明选择配对鸽子的刺激几乎没有持久效果：反应再次被吸引到游戏的平衡。结果证实了早期的发现，表明斯金纳的正强化原理与纳什数学一起完全解释了迭代博弈论行为。他们将这些发现扩展到所谓的自由操作：强化计划，其中反应不受刺激-反应顺序（即试验程序）的限制。这里介绍的耦合强化计划为经济和社会行为的实验分析提供了重要的希望。