Economic Theory Bulletin

, Volume 5, Issue 1, pp 119–126 | Cite as

A remark on discontinuous games with asymmetric information and ambiguity

Research Article

Abstract

We consider discontinuous games with asymmetric information and ambiguity (i.e., players have maximin preferences à la Gilboa and Schmeidler (1989)). It is shown that the existence of equilibria follows directly from the existence of Nash equilibria in every ex post game if all players are endowed with the maximin preferences. This is false for discontinuous games where players have Bayesian preferences as shown in He and Yannelis (2015a).

Keywords

Discontinuous game Asymmetric information Ambiguity Maximin expected utility 

Mathematics Subject Classification

C62 D81 D82 

References

  1. Angelopoulos, A., Koutsougeras, L.C.: Value allocation under ambiguity. Econ. Theory 59, 147–167 (2015)CrossRefGoogle Scholar
  2. Carbonell-Nicolau O., McLean, R.P.: On the existence of Nash equilibrium in Bayesian games, working paper, Rutgers University (2015)Google Scholar
  3. Carmona, G.: Reducible equilibrium properties: comments on recent existence results. Econ. Theory 61, 431–455 (2016)CrossRefGoogle Scholar
  4. Carmona, G., Podczeck, K.: Existence of Nash equilibrium in ordinal games with discontinuous preferences. Econ. Theory 61, 457–478 (2016)CrossRefGoogle Scholar
  5. de Castro, L.I., Liu, Z., Yannelis,N.C.: Implementation under ambiguity, Games Econ. Behav., forthcoming. doi:10.1016/j.geb.2015.10.010
  6. de Castro, L.I., Pesce, M., Yannelis, N.C.: Core and equilibria under ambiguity. Econ. Theory 48, 519–548 (2011)CrossRefGoogle Scholar
  7. de Castro, L.I., Yannelis, N.C.: Ambiguity aversion solves the conflict between efficiency and incentive compatibility, working paper (2009)Google Scholar
  8. Ellsberg, D.: Risk, ambiguity, and the Savage axioms. Quart. J. Econ. 75, 643–669 (1961)CrossRefGoogle Scholar
  9. Flesch, J., Predtetchinski, A.: Subgame-perfect \(\epsilon \)-equilibria in perfect information games with sigma-discrete discontinuities. Econ. Theory 61, 479–495 (2016)CrossRefGoogle Scholar
  10. Gilboa, I., Schmeidler, D.: Maximin expected utility with non-unique prior. J. Math. Econ. 18, 141–153 (1989)CrossRefGoogle Scholar
  11. Guo, H., Yannelis, N.C.: Robust and ambiguous implementation, working paper, University of Iowa (2016)Google Scholar
  12. He, W., Yannelis, N.C.: Discontinuous games with asymmetric information: an extension of Reny’s existence theorem. Games Econ. Behav. 91, 26–35 (2015a)CrossRefGoogle Scholar
  13. He, W., Yannelis, N.C.: Equilibrium theory under ambiguity. J. Math. Econ. 61, 86–95 (2015b)CrossRefGoogle Scholar
  14. He, W., Yannelis, N.C.: Existence of equilibria in discontinuous Bayesian games. J. Econ. Theory 162, 181–194 (2016a)Google Scholar
  15. He, W., Yannelis, N.C.: Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences. Econ. Theory 61, 497–513 (2016b)CrossRefGoogle Scholar
  16. Liu, Z.: Implementation of maximin rational expectations equilibrium, Econ. Theory, forthcoming. doi:10.1007/s00199-015-0932-5
  17. Nessah, R., Tian, G.: On the existence of Nash equilibrium in discontinuous games. Econ. Theory 61, 515–540 (2016)CrossRefGoogle Scholar
  18. Prokopovych, P.: Majorized correspondences and equilibrium existence in discontinuous games. Econ. Theory 61, 541–552 (2016)CrossRefGoogle Scholar
  19. Reny, P.J.: On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67, 1029–1056 (1999)CrossRefGoogle Scholar
  20. Reny, P.J.: Introduction to the symposium on discontinuous games. Econ. Theory 61, 423–429 (2016a)CrossRefGoogle Scholar
  21. Reny, P.J.: Nash equilibrium in discontinuous games. Econ. Theory 61, 553–569 (2016b)CrossRefGoogle Scholar
  22. Reny, P.J.: Equilibrium in discontinuous games without complete or transitive preferences. Econ. Theory Bull. 4, 1–4 (2016c)CrossRefGoogle Scholar
  23. Scalzo, V.: Remarks on the existence and stability of some relaxed Nash equilibrium in strategic form games. Econ. Theory 61, 571–586 (2016)CrossRefGoogle Scholar

Copyright information

© Society for the Advancement of Economic Theory 2016

Authors and Affiliations

  1. 1.Department of Economics, Henry B. Tippie College of BusinessThe University of IowaIowa CityUSA

Personalised recommendations