Solving payoff sets of perfect public equilibria: an example

Du, Chuang (2012): Solving payoff sets of perfect public equilibria: an example.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: repeated games; imperfect public monitoring; equilibrium payoff sets; duopoly
• Subjects: D - Microeconomics > D2 - Production and Organizations > D21 - Firm Behavior: Theory; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L15 - Information and Product Quality ; Standardization and Compatibility; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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