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The Many Faces of Rationalizability

  • Krzysztof R. Apt
Published/Copyright: May 24, 2007
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 7 Issue 1

The rationalizability concept was introduced in Bernheim [Ber84] and Pearce [Pea84] to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number of ways that differ in seemingly unimportant minor details. We shed light on these differences, explain their impact, and clarify for which games these definitions coincide.Then we apply the same analysis to explain the differences and similarities between various ways the iterated elimination of strictly dominated strategies was defined in the literature. This allows us to clarify the results of Dufwenberg and Stegeman [DS02] and Chen, Long and Luo [CLL05] and improve upon them. We also consider the extension of these results to strict dominance by a mixed strategy.Our approach is based on a general study of the operators on complete lattices. We allow transfinite iterations of the considered operators and clarify the need for them. The advantage of such a general approach is that a number of results, including order independence for some of the notions of rationalizability and strict dominance, come for free.

Keywords: rationalizability; iterated elimination of strategies; strict dominance; monotonicity
Published Online: 2007-5-24

©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston

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  1. Topics Article
  2. Equilibria in Multi-Unit Discriminatory Auctions
  3. A Note on Generating Globally Regular Indirect Utility Functions
  4. Value Maximization as an Ex-Post Consistent Firm Objective When Markets are Incomplete
  5. On Corruption and Institutions in Decentralized Economies
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  7. First-Degree Discrimination by a Duopoly: Pricing and Quality Choice
  8. Interbank Competition with Costly Screening
  9. Taxes versus Permits in a Two-Stage Duopoly
  10. The Many Faces of Rationalizability
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  12. Price Interventions in a Cournot Oligopoly with a Dominant Firm
  13. Mixed Oligopoly under Demand Uncertainty
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  30. Staged Financing with a Variable Return
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  43. Contests with Ties
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  45. Advances Article
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https://doi.org/10.2202/1935-1704.1339
Keywords for this article
rationalizability; iterated elimination of strategies; strict dominance; monotonicity

Articles in the same Issue

  1. Topics Article
  2. Equilibria in Multi-Unit Discriminatory Auctions
  3. A Note on Generating Globally Regular Indirect Utility Functions
  4. Value Maximization as an Ex-Post Consistent Firm Objective When Markets are Incomplete
  5. On Corruption and Institutions in Decentralized Economies
  6. Best Agendas in Multi-Issue Bargaining
  7. First-Degree Discrimination by a Duopoly: Pricing and Quality Choice
  8. Interbank Competition with Costly Screening
  9. Taxes versus Permits in a Two-Stage Duopoly
  10. The Many Faces of Rationalizability
  11. Cross and Double Cross: Comparative Statics in First Price and All Pay Auctions
  12. Price Interventions in a Cournot Oligopoly with a Dominant Firm
  13. Mixed Oligopoly under Demand Uncertainty
  14. Tacit Collusion in Capacity Investment: The Role of Capacity Exchanges
  15. Tax Differentials and the Segmentation of Networks of Cooperation in Oligopoly
  16. When Does Competition Lead to Efficient Investments?
  17. Herding with Costly Observation
  18. Asymmetric Nash Bargaining with Surprised Players
  19. Competing Gatekeepers
  20. Monotone Comparative Statics in Ordered Vector Spaces
  21. Pareto Optima and Competitive Equilibria with Moral Hazard and Financial Markets
  22. Decreasing Relative Risk Premium
  23. Advertising as a Distortion of Social Learning
  24. Pricing Behavior of Multiproduct Retailers
  25. Auctions with Opportunistic Experts
  26. A Consistent Multidimensional Generalization of the Pigou-Dalton Transfer Principle: An Analysis
  27. On the Effect of Risk Aversion in Two-Person, Two-State Finance Economies
  28. Contributions Article
  29. Information Goods Upgrades: Theory and Evidence
  30. Staged Financing with a Variable Return
  31. A Decentralized Market for a Perishable Good
  32. Effective Scrappage Subsidies
  33. Sunspot Rational Beliefs Structures, Equilibria and Excess Volatility
  34. Repeated Auctions with the Right of First Refusal
  35. A Herding Perspective on Global Games and Multiplicity
  36. Bribery and Favoritism by Auctioneers in Sealed-Bid Auctions
  37. Oligopoly, Endogenous Monopolist and Product Quality
  38. When Can Manipulations be Avoided in Two-Sided Matching Markets? -- Maximal Domain Results
  39. Free Cash Flow and Managerial Entrenchment: A Continuous-Time Stochastic Control-Theoretic Model
  40. Collective Punishments: Incentives and Examinations in Organisations
  41. Von Neumann-Morgenstern Stable Set Bridges Time-Preferences to the Nash Solution
  42. Information-Invariant Equilibria of Extensive Games
  43. Contests with Ties
  44. Local Network Effects and Complex Network Structure
  45. Advances Article
  46. Relating Network Structure to Diffusion Properties through Stochastic Dominance
  47. Firm Size, Productivity, and Manager Wages: A Job Assignment Approach
  48. Rule-Based and Case-Based Reasoning in Housing Prices
  49. Market Entry Dynamics with a Second-Mover Advantage
  50. The Compensation Principle and the National Income Test
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