Du, Chuang (2012): Solving payoff sets of perfect public equilibria: an example.
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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|
|Original Title:||Solving payoff sets of perfect public equilibria: an example|
|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
|Depositing User:||Chuang Du|
|Date Deposited:||07. May 2012 12:51|
|Last Modified:||17. Mar 2015 16:17|
Abreu, Dilip; Pearce, David; Stacchetti, Ennio. Toward a Theory of Discounted Repeated Games with Imperfect Monitoring. Econometrica, 1990: vol. 58, no. 5, pp. 1041-1063.
Abreu, Dilip; Sannikov, Y. An Algorithm for Two Player Repeated Games with Perfect Monitoring. 2011. Working Paper, Princeton.
Athey, Susan; Bagwell, Kyle. Optimal Collusion with Private Information. RAND Journal of Economics, vol. 32, no. 3, 2001, pp. 428-465.
Cai, Hongbin; Obara, Ichiro. Firm Reputation and Horizontal Integration, Rand Journal of Economics, 2009, vol.40, pp.341-364.
Cripps, Martin W; Mailath, George J; Samuelson, Larry. Imperfect Monitoring and Impermanent Reputations. Econometrica, 2004: vol. 72, no. 2, pp. 407-432.
Foreman, Stephen Earl; Shea, Dennis G. Publication of Information and Market Response: The Case of Airline On-Time Performance Reports. Review of Industrial Organization, 1999: vol. 14, no. 2, pp. 147-162.
Fudenberg, Drew; Kreps, David M; Maskin, Eric S. Repeated Games with Long-run and Short-run Players. Review of Economic Studies, 1990: vol. 57, no. 4, pp. 555-573.
Fudenberg, Drew; Levine, David. Efficiency and Observability with Long-Run and Short-Run Players. Journal of Economic Theory, 1994: vol. 62, no. 1, pp. 103-135.
Fudenberg, Drew; Levine, David; Maskin, Eric. The Folk Theorem with Imperfect Public Information. Econometrica, 1994: vol. 62, no. 5, pp. 997-1039.
Fudenberg, Drew; Levine, David; Takahashi, Satoru. Perfect Public Equilibrium When Players Are Patient. Games and Economic Behavior, 2007: vol. 61, no. 1, pp. 27-49.
Fudenberg, Drew; Maskin, Eric. The Folk Theorem in Repeated Games with Discounting or with Incomplete Information. Econometrica, 1986: vol. 54, no. 3, pp. 533-554.
Holmstrom, Bengt. Moral Hazard in Teams. The Bell Journal of Economics, 1982: vol. 13, no. 2, pp. 324-340.
Horner, Johannes. Reputation and Competition. American Economic Review, 2002: vol. 92, no. 3, pp. 644-663.
Horner, Johannes; Sugaya, Takuo; Takahashi, Satoru; Vieille, Nicolas. Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→1 and a Folk Theorem. Econometrica. 2011: vol.79, no. 4, pp. 1277-1318.
Horner, Johannes; Takahashi, Satoru; Vieille, Nicolas. On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games. 2012. COWLES Foundation Discussion Paper No.1848.
Judd, Kenneth L. Numerical Methods in Economics. The MIT Press, 1998.
Judd, Kenneth L; Yeltekin, Sevin; Conklin, James. Computing Supergame Equilibria. Econometrica, 2003: vol. 71, no. 4, pp. 1239-1254.
Klein, Benjamin; Leffler, Keith B. The Role of Market Forces in Assuring Contractual Performance. Journal of Political Economy, 1981: vol. 89, pp.615-641.
Kreps, David M; Wilson, Robert. Reputation and Imperfect Information. Journal of Economic Theory, 1982: vol. 27, no. 2, pp. 253-279.
Milgrom, Paul; Roberts, John. Predation, Reputation, and Entry Deterrence. Journal of Economic Theory, 1982: vol. 27, no. 2, pp. 280-312.
Nelson, Phillip. Information and Consumer Behavior. Journal of Political Economy, 1970: vol. 78, no. 2, pp. 311-329.
Rob, Rafael; Fishman, Arthur. Is Bigger Better? Customer Base Expansion through Word-of-Mouth Reputation. Journal of Political Economy, 2005: vol. 113, no. 5, pp. 1146-1162.
Rob, Rafael; Sekiguchi, Tadashi. Reputation and Turnover. RAND Journal of Economics, 2006: vol. 37, no. 2, pp. 341-361.
Shapiro, Carl. Premiums for High Quality Products as Returns to Reputations. Quarterly Journal of Economics, 1983: vol. 98, no. 4, pp. 659-679.
Sorin, S. On Repeated Games with Complete Information. Mathematics of Operations Research, 1986: vol 11, pp.147-160.
Suzuki, Yoshinori. The Relationship between On-Time Performance and Airline Market Share: A New Approach. Transportation Research: Part E: Logistics and Transportation Review, 2000: vol. 36, no. 2, pp. 139-154.
Wang, Cheng. Dynamic Insurance with Private Information and Balanced Budgets. Review of Economic Studies, 1995: vol. 62, no. 4, pp. 577-595.
Yamamoto, Y. The Use of Public Randomization in Discounted Repeated Games. International Journal of Game Theory, 2010: vol.39, pp.431-443.