arXiv subjects

Ichiro Obara

Publications and source records attributed to Ichiro Obara.

3 recordsLinked to original sources

arXiv2024

Weighted Garbling

We introduce an information order on experiments based on weighted garbling, a generalization of the standard notion of garbling. In this order, an experiment is more informative than another if the latter is a weighted garbling of the former. We show that this is equivalent to ordinary garbling conditional on a payoff-irrelevant event. We also characterize the order in terms of induced posterior belief distributions, showing that it depends only on their support. Our main results provide two decision-theoretic characterizations of this order. First, in static decision problems, one experiment dominates another if and only if its value of information is at least a fixed fraction of the other's across all problems. Second, in a class of stopping time problems with a hidden Markov process and repeated experimentation, one experiment dominates another if and only if it yields weakly higher expected payoffs for every problem with a regular prior.

econ.TH↗

arXiv2024

Uniformly Strict Equilibrium for Repeated Games with Private Monitoring and Communication

Cooperation through repetition is an important theme in game theory. In this regard, various celebrated ``folk theorems'' have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient attention paid to the robustness of a large set of equilibria that is needed for such folk theorems. Starting with perfect public equilibrium as our starting point, we study uniformly strict equilibria in repeated games with private monitoring and direct communication (cheap talk). We characterize the limit equilibrium payoff set and identify the conditions for the folk theorem to hold with uniformly strict equilibrium.

econ.TH↗

arXiv2023

Asymptotic Value of Monitoring Structures in Stochastic Games

This paper studies how improved monitoring affects the limit equilibrium payoff set for stochastic games with imperfect public monitoring. We introduce a simple generalization of Blackwell garbling called weighted garbling in order to compare different monitoring structures for this class of games. Our main result is the monotonicity of the limit perfect public equilibrium (PPE) payoff set with respect to this information order. We show that the limit PPE payoff set expands when the monitoring structure gets more informative with respect to the weighted garbling order. We also show that a similar monotonicity holds for strongly symmetric equilibrium for symmetric stochastic games. Finally, we show that our weighted garbling order is useful to compare the limit PPE payoff set for different state transition laws and monitoring structures when the limit feasible payoff set is the same.

econ.TH↗