Abstract
In this paper, we continue to explore the equilibrium theory under ambiguity. For a model of a pure exchange and asymmetric information economy with a measure space of agents whose exogenous uncertainty is described by a complete probability space, we establish a representation theorem for a Bayesian or maximin rational expectations equilibrium allocation in terms of a state-wise Walrasian equilibrium allocation. This result strengthens the theorems on the existence and representation of a (Bayesian) rational expectations equilibrium or a maximin rational expectations equilibrium in the literature.
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Notes
The concavity assumption in Bhowmik et al. (2014) can be easily replaced with our assumption (A \(_7\)) as it yields the quasi-concavity of each state-dependent utility function. Theorem 5.5 in Bhowmik et al. (2014) still holds under quasi-concavity of utility functions, since this assumption, along with continuity, monotonicity and availability assumptions, guarantees the existence of an equilibrium in each \({\mathscr {E}}(\omega )\).
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Bhowmik, A., Cao, J. Rational expectations equilibria: existence and representation. Econ Theory Bull 4, 367–386 (2016). https://doi.org/10.1007/s40505-016-0103-2
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DOI: https://doi.org/10.1007/s40505-016-0103-2
Keywords
- Asymmetric information
- Bayesian rational expectations equilibrium
- Maximin rational expectations equilibrium
- Pure exchange economy
- Walrasian equilibrium