Information Sharing in Linear Quadratic Games

We study the bilateral exchange of information in the context of linear quadratic games. An information structure is here represented by a non directed network, whose nodes are agents and whose links represent sharing agreements. We first study the equilibrium use of information given the network, finding that the extent to which a piece of information is observed by others affects the equilibrium use of it, in line with previous results in the literature. We then study the incentives to share information ex-ante, highlighting the role of the elasticity of payoffs to the equilibrium volatility of one\u2019s own strategy and of opponents\u2019 strategies. For the case of uncorrelated signals we fully characterise pairwise stable networks for the general linear quadratic game. For the case of correlated signals, we study pairwise stable networks for three specific linear quadratic games\u2014Cournot Oligopoly, Keynes\u2019 Beauty Contest and a Public Good Game\u2014in which strategies are substitute, complement and orthogonal, respectively. We show that signals\u2019 correlation favours the transmission of information, but may also prevent all information from being transmitted