The Speed of Learning in Noisy Games: Partial Reinforcement and the Sustainability of Cooperation

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Abstract
In an experiment, players' ability to learn to cooperate in the repeated prisoner's dilemma was substantially diminished when the payoffs were noisy, even though players could monitor one another's past actions perfectly. In contrast, in one-time play against a succession of opponents, noisy payoffs increased cooperation, by slowing the rate at which cooperation decays. These observations are consistent with the robust observation from the psychology literature that partial reinforcement (adding randomness to the link between an action and its consequences while holding expected payoffs constant) slows learning. This effect is magnified in the repeated game: when others are slow to learn to cooperate, the benefits of cooperation are reduced, which further hampers cooperation. These results show that a small change in the payoff environment, which changes the speed of individual learning, can have a large effect on collective behavior. And they show that there may be interesting comparative dynamics that can be derived from careful attention to the fact that at least some economic behavior is learned from experience.