Efficiency in games with Markovian private information (Q2871442)

Repeated Bayesian games with discounting, publicly observable actions, privately observable payoffs, or players' types, and communication are considered. The types evolve according to irreducible Markov chains whose transitions are independent across players. Players communicate with each other sending information on their current types but this information may be not truthful.NEWLINENEWLINEIt is well known that if players' types are independently and identically distributed over time, repeated play can facilitate cooperation beyond what is achievable in a one-shot interaction. In particular, the first-best efficiency can be approximately achieved as the discount factor goes to 1.NEWLINENEWLINEIn the article, this result is generalized to the considered serially dependent types. The main result implies that any Pareto-efficient payoff vector above the stationary minimax value can be approximately achieved in a perfect Bayesian equilibrium as the discount factor goes to 1. The proof uses an approximately efficient dynamic mechanism without assuming transferable utility.