On Team Guessing with Independent Information

Team theory is the study of situations in which a set of cooperating agents, called a team, each with access to different data or information, attempt to optimize a common criterion, under rules which restrict communication between agents. Team theory is of interest in theoretical studies in economics, communication and control.

A very simple example of a team situation is the following. Each of the team's n agents attempts to ascertain whether or not a certain random event E of probability ½ has occurred. Agent i must base his decision solely on the observation of random variable U_i and the team's goal is to minimize p̄ = n⁻¹ ∑p_i, where p_i is the probability that agent i makes an error. The main result of this paper is to show that when the variables U₁, …, U_n are independent, this alone places a positive lower bound on p̄, no matter what the joint distribution of E and the data {U_i} may be.

For each n the exact lower bound is determined: it is for n = 2, ¼ for n = 3 and as n goes to infinity it is asymptotic to