Irrational agents are driven out of the market by the rational ones. Intuitively, this mechanism should favor learning : irrational agents observing that rational agents are being more successful should adopt the same beliefs as the most successful ones. In this note, we show that the threat of elimination is not suffcient to push the agents towards rationality: a shorter "life" might be more rewarding than a longer one. More precisely, in a model with rational and irrational agents, we show that there are situations where irrational agents might rationally stay irrational in the sense that their ex-ante and ex-post welfare levels over their whole life are higher than (1) the welfare level that they would reach if they adopted rational expectations, (2) the welfare level reached by the rational agents, (3) the welfare level that they would have if they suddenly had the opportunity to swap their optimal allocation against the optimal allocation of a rational agents.
In both arbitrage and utility pricing approaches, the fictitious completion appears as a very powerful tool that permits to generalize to an incomplete markets framework, results initially established in a complete markets setting. does this technique permit to characterize the equilibrium pricing interval ? In other words, does the set of prices that can be reached at the equilibrium for at least one distribution of preferences/endowments and for at least one completion coincide with the set of prices that can be reached at the equilibrium for at least one distribution of preferences/endowments? This note provides a negative answer.
We analyze a model with two types of agents: standard agents and gurus, i.e. agents who have the ability to ináuence the other investors. Gurus announce their beliefs and act accordingly. Gurus are strategic: they take into account the impact of their announced Walras mechanism. The competition among gurus for attracting followers among standard agents is described by a simple dynamics and we focus on its steady states. At the equilibrium, this leads to beliefs heterogeneity, to a positive correlation between optimism and risk aversion and to higher risk premia. The impact is stronger on the riskier assets.
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