Economic Theory Bulletin

, Volume 6, Issue 2, pp 183–199 | Cite as

The maximin equilibrium and the PBE under ambiguity

  • Dionysius Glycopantis
  • Nicholas C. Yannelis
Research Article


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.


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

JEL Classification

D51 D61 D81 D82 



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.


  1. Angelopoulos, A., Koutsougeras, L.C.: Value allocation under ambiguity. Econ. Theory 59(1), 147–167 (2015)CrossRefGoogle Scholar
  2. de Castro, L.I., Yannelis, N.C.: Ambiguity aversion solves the conflict between efficiency and incentive compatibility. Working Paper (2009)Google Scholar
  3. de Castro, L.I., Yannelis, N.C.: An interpretation of Ellsberg’s Paradox based on information and incompleteness. Econ. Theory Bull. 1(2), 139–144 (2013)CrossRefGoogle Scholar
  4. de Castro, L.I., Pesce, M., Yannelis, N.C.: Core and equilibria under ambiguity. Econ. Theory 48, 519–548 (2011)CrossRefGoogle Scholar
  5. de Castro, L.I., Liu, Z., Yannelis, N.C.: Implementation under ambiguity. Games Econ. Behav. (2015). CrossRefGoogle Scholar
  6. de Castro, L.I., Liu, Z., Yannelis, N.C.: Ambiguous implementation: the partition model. Econ. Theory 63, 233–261 (2017). CrossRefGoogle Scholar
  7. Glycopantis, D., Muir, A., Yannelis, N.C.: An extensive form interpretation of the private core. Econ. Theory 18, 293–319 (2001)CrossRefGoogle Scholar
  8. Glycopantis, D., Muir, A., Yannelis, N.C.: On extensive form implementation of contracts in differential information economies. Econ. Theory 21, 495–526 (2003)CrossRefGoogle Scholar
  9. He, W., Yannelis, N.C.: Equilibrium theory under ambiguity. J. Math. Econ. 61, 86–95 (2015)CrossRefGoogle Scholar
  10. Holmström, B., Myerson, R.B.: Efficient and durable decision rules with incomplete information. Econometrica 51(6), 1799–1819 (1983)CrossRefGoogle Scholar
  11. Liu, Z.: A note on the welfare of the maximin rational expectations. Econ. Theory Bull. 2, 213–218 (2014)CrossRefGoogle Scholar
  12. Palfrey, T.R., Srivastava, S.: On Bayesian implementable allocations. Rev. Econ. Stud. 54(2), 193–208 (1987)CrossRefGoogle Scholar
  13. Wald, A.: Statistical Decision Functions. Wiley, New York (1950)Google Scholar
  14. Yannelis, N.C.: The Core of an economy with differential information. Econ. Theory 1, 183–198 (1991)CrossRefGoogle Scholar

Copyright information

© Society for the Advancement of Economic Theory 2018

Authors and Affiliations

  1. 1.Department of EconomicsCity, University of LondonLondonUK
  2. 2.Department of Economics, Tippie College of BusinessUniversity of IowaIowa CityUSA

Personalised recommendations