Value of Persistent Information

Abstract

We develop a theory of how the value of an agent's information advantage depends on the persistence of information. We focus on strategic situations with strict conflict of interest, formalized as stochastic zero‐sum games where only one of the players observes the state that evolves according to a Markov operator. Operator Q is said to be better for the informed player than operator P if the value of the game under Q is higher than under P regardless of the stage game. We show that this defines a convex partial order on the space of ergodic Markov operators. Our main result is a full characterization of this partial order, intepretable as an ordinal notion of persistence relevant for games. The analysis relies on a novel characterization of the value of a stochastic game with incomplete information.

Informed-Principal Problem in Mechanisms with Limited Commitment

“…However, since the principal can commit ex ante, he can choose an ex-ante optimal mechanism and commit to ignore his private information. More information can hurt if the designer cannot commit not to use the additional piece of information, which is related to the ratchet effect in general and more recently Peski-Toikka (2017). And even if the offered mechanism reveals his private information, the mechanism designer can still commit in the beginning of the first period.…”

Truthful Equilibria in Dynamic Bayesian Games

“…It is known for p ∈ [1/2, 2/3] and some specific values Pęski and Toikka (2014). have recently shown that this value is non-increasing in p, andBressaud and Quas (2014) have determined the optimal strategies for values of p up to ∼ .7323.…”

Truthful Equilibria in Dynamic Bayesian Games

“…It is known for p ∈ [1/2 2/3] and some specific values Pęski and Toikka (2014). have recently shown that this value is nonincreasing in p, andBressaud and Quas (2014) have determined the optimal strategies for values of p up to ∼ 0 7323.…”