What restrictions do Bayesian games impose on the value of information?

In a Bayesian game players play an unknown game. Before the game starts some players may receive a signal regarding the specific game actually played. Typically, information structures that determine different signals, induce different equilibrium payoffs.In zero-sum games the equilibrium payoff measures the value of the particular information structure which induces it. We pose a question as to what restrictions do Bayesian games impose on the value of information. We provide answers in two kinds of information structures: symmetric, where both players are equally informed, and one-sided where only one player is informed.value of information, zero-sum, information structure, partition, Beyesian game

A Wide Range No-Regret Theorem

In a sequential decision problem at any stage a decision maker, based on the history, takes a decision and receives a payoff which depends also on the realized state of nature. A strategy, f, is said to be as good as an alternative strategy g at a sequence of states, if in the long run f does, on average, at least as well as g does. It is shown that for any distribution, P, over the alternative strategies there is a strategy f which is, at any sequence of states, as good as P-almost any alternative g.No-regret, Approachability, large spaces

Information and Its Value in Zero-Sum Repeated Games

Two players play an unknown zero-sum repeated game. Before the game starts one player may receive signals, whose nature is specified by an information structure, regarding the game actually played. We characterize when one information structure is better for the maximizer than another. We also characterize those functions defined on partitions that determine the equilibrium payoff when one player is informed about the cell of the partition that contains the realized state.value of information, repeated games

On the Optimal Amount of Experimentation in Sequential Decision Problems

We provide a tight bound on the amount of experimentation under the optimal strategy in sequential decision problems. We show the applicability of the result by providing a bound on the cut-off in a one-arm bandit problem

Approximating a sequence of observations by a simple process

Given a sequence (s0; s1,..., sN) of observations from a finite set S, we construct a process (sn)n_Markov chains; approximation theory