We study a class of games where players face restrictions on how much information they can obtain on a common payoff-relevant state, but have some leeway in covertly choosing the dependence between their signals, before simultaneously choosing actions. Using a new stochastic dependence ordering between signals, we show that each player chooses information that is more dependent on the information of other players whose actions are either isotonic and complements with his actions or antitonic and substitutes with his actions. Similarly, each player chooses information that is less dependent on the information of other players whose actions are antitonic and complements with his actions or isotonic and substitutes with his actions. We then provide sucient conditions for information structures such as public or private information to arise in equilibrium. Equilibrium information structures may be inefficient. Making which signals were chosen (but not their realizations) publicly observable may restore efficiency.