Stochastic Control Approach to Reputation Games

DALKIRAN N. A., Yuksel S.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, cilt.65, sa.11, ss.4710-4725, 2020 (SCI-Expanded, SSCI, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 11
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1109/tac.2020.2968861
  • Dergi Adı: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.4710-4725
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

Through a stochastic-control-theoretic approach, we analyze reputation games, where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the information of the short-lived players is nested in that of the long-lived player. This nested information structure is obtained through an appropriate monitoring structure. Under this monitoring structure, we show that, given mild assumptions, the set of perfect Bayesian equilibrium payoffs coincides with Markov perfect equilibrium payoffs, and hence, a dynamic programming formulation can be obtained for the computation of equilibrium strategies of the strategic long-lived player in the discounted setup. We also consider the undiscounted average-payoff setup, where we obtain an optimal equilibrium strategy of the strategic long-lived player under further technical conditions. We then use this optimal strategy in the undiscounted setup as a tool to obtain a tight upper payoff bound for the arbitrarily patient long-lived player in the discounted setup. Finally, by using measure concentration techniques, we obtain a refined lower payoff bound on the value of reputation in the discounted setup. We also study the continuity of equilibrium payoffs in the prior beliefs.