We provide a discipline for beliefs formation through a model of subjective beliefs, in which agents hold incorrect but strategic beliefs. More precisely, we consider beliefs as a strategic variable that agents can manipulate to maximize their utility from trade. Our framework is therefore an imperfect competition framework, and the underlying concept is the concept of Nash equilibrium. We find that a strategic behavior leads to beliefs subjectivity and heterogeneity. Optimism (resp. overconfidence) as well as pessimism (resp. doubt) both emerge as optimal beliefs. Furthermore, we obtain a positive correlation between pessimism (resp. doubt) and risk-tolerance. The consensus belief is pessimistic and, as a consequence, the risk premium is higher than in a standard setting. Our model is embedded in a standard financial markets equilibrium problem and may be applied to several other situations in which agents have to choose the optimal exposure to a risk (choice of an optimal retention rate for an insurance company, choice of the optimal proportion of equity to retain for an entrepreneur and for a given project).
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