# The maximin equilibrium and the PBE under ambiguity

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## Abstract

This note refers to the recent work on ambiguous implementation by de Castro–Liu–Yannelis (Econ Theory 63:233–261, 2017). The authors discuss, under condition of ambiguity, the implementation as maximin equilibria of maximin individually rational and ex ante maximin efficient allocations. An explicit example is used to support their analysis. We analyse further the example used by de Castro–Liu–Yannelis (2017). We show that in the formulated game tree the proposed allocation is implementable through a backward induction argument. Also it is shown that a perfect Bayesian equilibrium (PBE) exists, leading to different allocations. Comparisons are drawn between the maximin and the PBE implementations. We consider also briefly the meaning of the incentive compatibility (IC) of proposed allocations.

## Keywords

Ambiguity Maximin preferences Maximin efficient allocations Maximin equilibrium Implementation Mechanism design Perfect Bayesian equilibrium Nash equilibrium## JEL Classification

D51 D61 D81 D82## Notes

### Acknowledgements

Very helpful comments by Zhiwei Liu on earlier drafts were greatly appreciated. We are also very grateful to a referee for very helpful comments. Of course all inadequacies are our responsibility.

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