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Models of stochastic choice are studied in decision theory, discrete choice econometrics, behavioral economics and psychology. Numerous experiments show that perception of stimuli is not deterministic, but stochastic (randomly determined). A growing body of evidence indicates that the same is true of economic choices. Whether trials are separated by days or minutes, the fraction of choice reversals is substantial. Stochastic Choice Theory offers a systematic introduction to these models, unifying insights from various fields. It explores mathematical models of stochastic choice, which have a variety of applications in game theory, industrial organization, labor economics, marketing, and experimental economics. Offering a systematic introduction to the field, this book builds up from scratch without any prior knowledge requirements and surveys recent developments, bringing readers to the frontier of research.