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Sentiments and rationalizability

Mathevet, Laurent (2010): Sentiments and rationalizability.

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Sentiments are characteristics of players' beliefs. I propose two notions of sentiments, confidence and optimism, and I study their role in shaping the set of rationalizable strategy profiles in (incomplete information) games with complementarities. Confidence is related to a player's perceived precision of information; optimism is the sentiment that the outcome of the game will be ``favorable.'' I prove two main results on how sentiments and payoffs interact to determine the size and location of the set of rationalizable profiles. The first result provides an explicit upper bound on the size of the set of rationalizable strategy profiles, relating complementarities and confidence; the second gives an explicit lower bound on the change of location, relating complementarities and optimism. I apply these results to four areas. In models of currency crisis, the results suggest that the most confident investors may drive financial markets. In models of empirical industrial organization, the paper provides a classification of the parameter values for which the model is identified. In non-Bayesian updating, the results clarify the strategic implications of certain biases. Finally, the results generalize and clarify the uniqueness result of global games.

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