It is well known that sequential decision making may lead to information cascades. That is, when agents make decisions based on their private information, as well as observing the actions of those before them, then it might be rational to ignore their private signal and imitate the action of previous individuals. If the individuals are choosing between a right and a wrong state, and the initial actions are wrong, then the whole cascade will be wrong. This issue is due to the fact that cascades can be based on very little information. We show that if agents occasionally disregard the actions of others and base their action only on their private information, then wrong cascades can be avoided. Moreover, we study the optimal asymptotic rate at which the error probability at time @math can go to zero. The optimal policy is for the player at time @math to follow their private information with probability @math , leading to a learning rate of @math , where the constants @math and @math are explicit.
One possible source of additional information comes from people not acting in a rational, Bayesian manner. It is well documented that human behavior is often irrational (see, e.g., @cite_13 ). In the information cascades setting, laboratory experiments by Anderson and Holt @cite_4 show that while most participants act rationally, many do not. When deviations from rational behavior occur, participants often act mainly or solely based on their private information, disregarding the information in the actions of those before them. See also related experiments and results by C elen and Kariv @cite_8 for a setting with continuous signals. Such individuals effectively reveal their private signal, which is valuable information for those coming after them. The model described in , which contains and , captures this empirically observed behavioral phenomenon.
@cite_13 @cite_4 @cite_8
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When a series of individuals with private information announce public predictions, initial conformity can create an 'information cascade' in which later predictions match the early announcements. This paper reports an experiment in which private signals are draws from an unobserved urn. Subjects make predictions in sequence and are paid if they correctly guess which of two urns was used for the draws. If initial decisions coincide, then it is rational for subsequent decisionmakers to follow the established pattern, regardless of their private information. Rational cascades formed in most periods in which such an imbalance occurred. Copyright 1997 by American Economic Association. Humans are adept at inferring the mental states underlying other agents’ actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents’ behavior based on the principle of rationality: the expectation that agents will plan approximately rationally to achieve their goals, given their beliefs about the world. The mental states that caused an agent’s behavior are inferred by inverting this model of rational planning using Bayesian inference, integrating the likelihood of the observed actions with the prior over mental states. This approach formalizes in precise probabilistic terms the essence of previous qualitative approaches to action understanding based on an ‘‘intentional stance” [Dennett, D. C. (1987). The intentional stance. Cambridge, MA: MIT Press] or a ‘‘teleological stance” [Gergely, G., Nadasdy, Z., Csibra, G., & Biro, S. (1995). Taking the intentional stance at 12 months of age. Cognition, 56, 165–193]. In three psychophysical experiments using animated stimuli of agents moving in simple mazes, we assess how well different inverse planning models based on different goal priors can predict human goal inferences. The results provide quantitative evidence for an approximately rational inference mechanism in human goal inference within our simplified stimulus paradigm, and for the flexible nature of goal representations that human observers can adopt. We discuss the implications of our experimental results for human action understanding in real-world contexts, and suggest how our framework might be extended to capture other kinds of mental state inferences, such as inferences about beliefs, or inferring whether an entity is an intentional agent. This paper reports an experimental test of how individuals learn from the behavior of others. By using techniques only available in the laboratory, we elicit subjects' beliefs. This allows us to distinguish informational cascades from herd behavior. By adding a setup with continuous signal and discrete action, we enrich the ball-andurn observational learning experiments paradigm of Lisa R. Anderson and Charles Holt (1997). We attempt to understand subjects' behavior by estimating a model that allows for the possibility of errors in earlier decisions. Most human behaviors consist of multiple parts, steps, or sub-tasks. These structures guide our action planning and execution, but when we observe others, the latent structure of their actions is typically unobservable, and must be inferred in order to learn new skills by demonstration, or to assist others in completing their tasks. For example, an assistant who has learned the subgoal structure of a colleague's task can more rapidly recognize and support their actions as they unfold. Here we model how humans infer subgoals from observations of complex action sequences using a nonparametric Bayesian model, which assumes that observed actions are generated by approximately rational planning over unknown subgoal sequences. We test this model with a behavioral experiment in which humans observed different series of goal-directed actions, and inferred both the number and composition of the subgoal sequences associated with each goal. The Bayesian model predicts human subgoal inferences with high accuracy, and significantly better than several alternative models and straightforward heuristics. Motivated by this result, we simulate how learning and inference of subgoals can improve performance in an artificial user assistance task. The Bayesian model learns the correct subgoals from fewer observations, and better assists users by more rapidly and accurately inferring the goal of their actions than alternative approaches.