Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 31: Evolutionary Game Theory and Economic Models (joint session SOE/ BP/ DY)
DY 31.3: Talk
Thursday, April 3, 2014, 11:30–11:45, GÖR 226
Differential value of information in non-cooperative games — Nils Bertschinger1, David H. Wolpert2, •Eckehard Olbrich1, and Jürgen Jost1,2 — 1Max Planck Institut für Mathematik in den Naturwissenschaften, Leipzig — 2Santa Fe Institute, NM, USA
We study how players value changes in the information structure of non-cooperative games with imperfect information.
We use the functionals central to Shannon's information theory to quantify amounts of information study how changes in the values of those functionals are related to changes in the expected utility of the players. Our approach is based on the Multi-Agent Influence Diagram representation of games, and is based on a generalization of the concept of marginal utility in decision scenarios to apply to infinitesimal changes of the channel parameters in non-cooperative games. Using that framework we derive general conditions for the possibility of a negative value of information, and show that generically, these conditions hold in all games unless one imposes a priori constraints on the allowed changes to information channels. In other words, in any game in which a player values some aspect of the game's specification beyond the information provided in that game, there will be an infinitesimal change to the parameter vector specifying the game that increases the information but hurts the player.
We demonstrate these results numerically for a leader-follower game and discuss their general implications.