Comparison of information structures

We introduce two ways of comparing information structures, say ${\cal I}$ and ${\cal J}$. First we say that ${\cal I}$ is richer than ${\cal J}$ when for every compact game $G$, all correlated equilibrium distributions of $G$ induced by ${\cal J}$ are also induced by ${\cal I}$. Second, we say that ${\cal J}$ is faithfully reproducable from ${\cal I}$ when all the players can compute from their information in ${\cal I}$ ``new information'' that they could have received from ${\cal J}$. We prove that ${\cal I}$ is richer than ${\cal J}$ if and only if ${\cal J}$ is faithfully reproducable from ${\cal I}$.Game--theory, information, correlation

A reasoning approach to introspection and unawareness

We introduce and study a unified reasoning process which allows to represent the beliefs of both a fully rational agent and of an unaware one. This reasoning process provides natural properties to introspection and unawareness. The corresponding model for the rational or boundedly rational agents is both easy to describe and to work with, and the agent’s full system of beliefs has natural descriptions using a reduced number of parameters.Economics (Jel: A)

When is the individually rational payoff in a repeated game equal to the minmax payoff?

We study the relationship between a player’s (stage game) minmax payoff and the individually rational payoff in repeated games with imperfect monitoring. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show that, if the monitoring structure of an infinitely repeated game ‘nearly’ satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.

Informational cascades elicit private information

We introduce cheap talk in a dynamic investment model with information externalities. We first show how social learning adversely affects the credibility of cheap talk messages. Next, we show how an informational cascade makes truthtelling incentive compatible. A separating equilibrium only exists for high surplus projects. Both an investment subsidy and an investment tax can increase welfare. The more precise the sender’s information, the higher her incentives to truthfully reveal her private information.Cheap Talk; Information Externality; Informational Cascades; Social Learning; Herd Behaviour

Entropy Bounds on Bayesian Learning.

An observer of a process View the MathML source believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(xt|x1,…,xt−1) and Q(xt|x1,…,xt−1) for t=1,…,n by a function of the relative entropy between the marginals of P and Q on the n first realizations. We apply this bound to the cost of learning in sequential decision problems and to the merging of Q to P.Bayesian learning; Repeated decision problem; Value of information; Entropy;

Informational Cascades Elicit Private Information

We introduce cheap talk in a dynamic investment model with information externalities. We first show how social learning adversely affects the credibility of cheap talk messages. Next, we show how an informational cascade makes thruthtelling incentive compatible. A separating equilibrium only exists for high surplus projects. Both an investment subsidy and an investment tax can increase welfare. The more precise the sender's information, the higher her incentives to truthfully reveal her private information.Cheap Talk, Information Externality, Informational Cascades, Social Learning, Herd Behaviour

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariate linear regressions, and compare their powers. This fills an important gap in the literature where the only known nonparametric tests are either asymptotic, or assume one covariate only.Exact, linear regression, nonparametric.

Repeated Communication Through the Mechanism And.

We consider the “and” communication device that receives inputs from two players and outputs the public signal yes if both messages are yes, and outputs no otherwise. We prove that no correlation can securely be implemented using this device, even when infinitely many stages of communication are allowed."And" communication device;

COORDINATION THROUGH DE BRUIJN SEQUENCES

Let µ be a rational distribution over a finite alphabet, and ( ) be a n-periodic sequences which first n elements are drawn i.i.d. according to µ. We consider automata of bounded size that input and output at stage t. We prove the existence of a constant C such that, whenever , with probability close to 1 there exists an automaton of size m such that the empirical frequency of stages such that is close to 1. In particular, one can take , where and .Coordination, complexity, De Bruijn sequences, automata

Impermanent Types and Permanent Reputations

We study the impact of unobservable stochastic replacements for the long-run player in the classical reputation model with a long-run player and a series of short-run players. We provide explicit lower bounds on the Nash equilibrium payoffs of a long-run player, both ex-ante and following any positive probability history. Under general conditions on the convergence rates of the discount factor to one and of the rate of replacement to zero, both bounds converge to the Stackelberg payoff if the type space is sufficiently rich. These limiting conditions hold in particular if the game is played very frequently.Reputation, repeated games, replacements, disappearing reputations JEL Classification Numbers: D80, C73