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Uniqueness in Two-type Signalling Games: Finite Response Sets vs. Continuum Response Sets

Author

Listed:
  • Svend Albæk

    (Institute of Economics, University of Copenhagen)

  • Per Baltzer Overgaard

    (Department of Economics, University of Aarhus)

Abstract

The paper considers signalling games with two types of informed player. When the informed player's payoff function satisfies certain sorting and type monotonicity conditions, and when the uninformed player's response is a smooth strictly monotone mapping from posterior beliefs, the results of Cho and Sobel (1990) establish existence of a unique refined equilibrium outcome which is separating. However, when the response set is finite, refined pooling equilibria generally exist. We consider the finite-response case, and our results are as follows: For every prior probability assessment over the two types there is a finite number of responses ¯n(?0), where ?0 is the prior weight on the "good" type, such that for every n = ¯n(?0) no pooling can be part of a refined equilibrium. I.e., if Nature chooses ?0 from some continuous probability distribution on the unit interval, then the probability that refined pooling equilibria exist goes to zero when n increases withut bound. In the limit the measure is zero as shown by Cho and Sobel.

Suggested Citation

  • Svend Albæk & Per Baltzer Overgaard, 1992. "Uniqueness in Two-type Signalling Games: Finite Response Sets vs. Continuum Response Sets," Discussion Papers 94-02, University of Copenhagen. Department of Economics, revised Feb 1994.
  • Handle: RePEc:kud:kuiedp:9402
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    More about this item

    Keywords

    signalling games; equilibrium refinement; uniqueness; finite response sets; continuum sets;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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