Resumen de The economics of information transmission

Penélope Hernández Rojas , Olivier Gossner, Abraham Neyman

• It is a well known phenomenon that communication between a group of players affects the set of equilibria of a repeated game. This communication can be costly. Its cost may be measured in terms of complexity, or payoffs.

  In particular, a payoff cost of communication occurs when players communicate through their actions, and one is interested in characterizing the optimal communication.

  We study a class of games that models the communication cost of online coordination. For example: A sequence X = (X(t)) of zeroes and ones is chosen at random, and announced to a player, the seer, but not to his teammate, the follower. A repeated game then proceeds in which the follower and the seer choose actions Y (t) and Z(t) in {0, 1} at stage t, and their (common) stage payoff is 1 whenever X(t) = Y (t) = Z(t).

  We address the question of the optimal communication level from the seer to the follower in order to maximize payoffs. We characterize this level using the notion of entropy, and provide construction of optimal strategies for the team: the seer and the follower. In particular, we prove that against a family of i.i.d. random variables (1/2, 1/2), the maximum expected payoff v to the team is the solution of the equation H(x) + log(3) (1 - x) = 1;

  where H is the entropy function and log is taken in basis 2. Moreover, we prove the existence of pure strategies of the prophet and the seer that guarantee v against all sequences X = X(t). Hence, the zero-sum game in which player I is the Team (no correlation is allowed between its members), player II is the opponent, and the payoff to I is as above, has a value, and this equals v. Our result has direct implications for repeated games played by finite automata, or by players with bounded recall.