Open AccessBounding equilibrium payoffs in repeated games with private monitoring
Author(s) -
Sugaya Takuo,
Wolitzky Alexander
Publication year - 2017
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/te2270
Subject(s) - stochastic game , bounding overwatch , mathematical economics , repeated game , set (abstract data type) , simple (philosophy) , upper and lower bounds , folk theorem , characterization (materials science) , mathematical optimization , preemption , mathematics , computer science , equilibrium selection , game theory , artificial intelligence , mathematical analysis , philosophy , materials science , operating system , epistemology , programming language , nanotechnology
We provide a simple sufficient condition for the existence of a recursive upper bound on (the Pareto frontier of) the sequential equilibrium payoff set at a fixed discount factor in two‐player repeated games with imperfect private monitoring. The bounding set is the sequential equilibrium payoff set with perfect monitoring and a mediator. We show that this bounding set admits a simple recursive characterization, which nonetheless necessarily involves the use of private strategies. Under our condition, this set describes precisely those payoff vectors that arise in equilibrium for some private monitoring structure if either nonstationary monitoring or communication is allowed.