Value of information in noncooperative games

TL;DR

This paper investigates how additional information can negatively impact players in noncooperative games, revealing that most games can have a negative value of information for players unless constrained.

Contribution

It introduces a generalized definition of marginal utility of information in games and proves that typically, games can exhibit negative value of information for players.

Findings

Most games can have negative marginal value of information.

Negative value of information can occur for all players in a game.

Numerical demonstrations support theoretical results.

Abstract

In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-mover's move. What properties of a game determine whether it has such negative "value of information" for a particular player? Can a game have negative value of information for all players? To answer such questions, we generalize the definition of marginal utility of a good to define the marginal utility of a parameter vector specifying a game. So rather than analyze the global structure of the relationship between a game's parameter vector and player behavior, as in previous work, we focus on the local structure of that relationship. This allows us to prove that generically, every game can have negative marginal value of information, unless one imposes a priori constraints on allowed changes to the game's parameter vector. We demonstrate these and related results numerically, and discuss their implications.