Open AccessTrust and betrayals: Reputational payoffs and behaviors without commitment
Author(s) -
Pei Harry
Publication year - 2021
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te4182
Subject(s) - stochastic game , stackelberg competition , mathematical economics , action (physics) , private information retrieval , betrayal , repeated game , ultimatum game , microeconomics , economics , game theory , computer science , psychology , social psychology , physics , computer security , quantum mechanics
I study a repeated game in which a patient player wants to win the trust of some myopic opponents, but can strictly benefit from betraying them. His benefit from betrayal is strictly positive and is his persistent private information. I characterize every type of patient player's highest equilibrium payoff and construct equilibria that attain this payoff. Since the patient player's Stackelberg action is mixed and motivating the lowest‐benefit type to play mixed actions is costly, every type's highest equilibrium payoff is strictly lower than his Stackelberg payoff. In every equilibrium where the patient player approximately attains his highest equilibrium payoff, no type of the patient player plays stationary strategies or completely mixed strategies.