Bray Theory Workshop

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 an ergodic 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, providing an ordinal notion of persistence relevant for games. Our main result is a full characterization of this partial order. The analysis relies on a novel characterization of the value of a stochastic game with incomplete information. Our results can be interpreted as pertaining to the minmax value in repeated Bayesian games with Markov types, in which case they imply that the limit equilibrium payoff set in such games is increasing in persistence.

Link to paper: http://economics.mit.edu/files/10916