The value of information in oligopoly with demand uncertainty

This paper discusses the value of information in supermodular and submodular games, using a simple duopoly model where the level of demand is uncertain. It is shown that the value of information is superadditive (resp., subadditive) between players if the game is supermodular (resp., submodular). For example, in a Bertrand (resp.. Cournot) market with (possibly imperfect) substitute products, one firms information acquisition increases (resp., decreases) the other firm's incentive to acquire the same information. Furthermore. when the game is either supermodular or submodular. the value of information is higher when the player is expected to be informed according to the opponent's belief than when the player is expected to he uninformed; this result is reversed when the game has asymmetric modularity (i.e,, one player's action is substitutional to the other's, and the latter's action is complemental to the former's). These qualitative observations have a potential to be applied to a larger class of games with uncertainty where payoffs are smooth (e.g., twice continuously differentiable) in actions and states.