Economists usually assume that decision makers know the consequences of their actions, form rational expectations, and possess internally consistent preferences. We do this in order to predict how people will behave in novel situations. When the situation is strategic, the knowledge assumptions needed to deduce a prediction are even stronger. Yet, people often have to make decisions without much information and at least as often ignore information that is readily available.

For example, it is difficult to communicate a common knowledge description of a game to undergraduate students. Moreover, we sometimes doubt that subjects in an experiment are actually using this information to deduce a mutually consistent way to behave. As Vernon Smith (1990, p12) wrote, "Many years of experimental research have made it plain that real people do not solve decision problems by thinking about them in the way we do as economic theorists. Only academics learn primarily by reading and thinking. Those who run the world, and support us financially, tend to learn by watching, listening, and doing. ... When experiments approximate the predictions of theory, it is because subjects experience the choices of others and then choose based on what they have learned to expect."

Van Huyck, Cook, and Battalio (1994) report an experiment rejecting the stability conditions derived from the myopic best response dynamic and find that stability conditions based on relaxation algorithms with inertia make more accurate predictions. They were careful to communicate the best response function to their subjects, since this information seemed central to the theory being tested. Smith’s observation suggests that the subjects’ knowledge of the best response function doesn’t explain why the theory made accurate predictions. Our research hypothesis is that taking away information only used in a deductive analysis of the situation, like the best response function, will not influence behavior since subjects don’t use it anyway.

Reinforcement learning algorithms only require that players know their feasible actions and respond to the consequences of their actual choices. These algorithms can also be used as selection theories, although convergence to a mutually consistent outcome is not guaranteed in general. This paper reports an experiment in which subjects are limited to the information used by reinforcement learning algorithms and contrasts the results with Van Huyck, Cook, and Battalio (1994).

The reinforcement learning algorithms considered below do not accurately predict observed behavior under reinforcement information conditions. Humans converge to the interior equilibrium at speeds that are orders of magnitude faster than the models. Observed behavior under complete information and reinforcement information treatments do differ in the length of time it takes to converge to a mutual best response outcome. However, all cohorts converged to the market statistic predicted by the interior equilibrium regardless of the information conditions or the stability conditions derived from the myopic best response dynamic. Average subject behavior did increase in exactly the way predicted by a conventional comparative static analysis.

The paper is organized as follows: Section II reviews Van Huyck, Cook, and Battalio’s (1994) analytical framework and the Cross Dynamic studied in Borgers, Morales, and Sarin (2001); Section III reports the experimental design; Section IV reports the experimental results; Section V estimates an empirical model of satisfaction; Section VI compares the complete and reinforcement information treatments; Section VII concludes with a discussion of low cognitive game theory and the problem of modeling imagination in light of our results.

All of this is true under both the complete and reinforcement information treatments. So there is a sense in which the hypothesis that taking away information only used in a deductive analysis of the situation will not influence behavior since subjects don’t use it anyway is not contradicted by the experiment. However, the information treatment does influence behavior in a subtle, but statistically significant way. It takes longer for the median to converge to the interior equilibrium median, the process is noisier under the reinforcement information treatment, and more subjects fail to give a best response to the median in the terminal period.

A careful analysis of the data reveals that random search models of reinforcement learning, like Erev and Roth (1995) or the closely related Cross Dynamic, do not accurately describe behavior even when subjects are restricted to reinforcement information. Specifically, our subjects are able to search the action space much more efficiently than the random-search-reinforcement-learning analysis allows. Our subjects do better even under information conditions that favor the reinforcement learning algorithm. It appears to us that human cognition is not well described by either the choice-theoretic analysis or the random-search-reinforcement-learning analysis.

Sarin and Vahid (2001) propose a payoff assessment model that takes account of the similarity amongst strategies to explain the data reported in this paper. Their payoff assessment model fits remarkably well and is more successful than the original Cross model and versions that include similarity or declining step size. Chen and Khoroshilov (2001) use the data reported in this paper to compare the payoff assessment model to a version of experience weighted attraction learning model and a version of the relative payoff sum model. They also find the payoff assessment model fits the data best.

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