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Solving payoff sets of perfect public equilibria: an example

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  • Du, Chuang

Abstract

We study an example of infinitely repeated games in which symmetric duopolistic firms produce experience goods. After consuming the products, short-run consumers only observe imperfect public information about product quality. We characterize perfect public equilibrium payoff set E(δ) of firms for each fixed discount factor δ∈[0,1) when each firm has two action choices, signals follow binomial distributions and the game has a product structure. The set E(δ) turns out a single point or symmetric pentagon for fixed δ. And δ∈[0, 1) can be divided into countable infinite subintervals in which E(δ) remains constant. The strategies to implement payoffs in boundaries of E(δ) are constructed in a recursive way, in which infinite repetition of Nash Equilibrium of stage game could be viewed as an absorbing state in a Markov Process where state transitions are controlled through public signals and optimal punishments in each period.

Suggested Citation

  • Du, Chuang, 2012. "Solving payoff sets of perfect public equilibria: an example," MPRA Paper 38622, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:38622
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    References listed on IDEAS

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    More about this item

    Keywords

    repeated games; imperfect public monitoring; equilibrium payoff sets; duopoly;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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