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 (or similarity) between their signals, before simultaneously choosing actions. Using a new dependence stochastic ordering between signals, we show that each player prefers and chooses information that is more dependent on the information of other players whose actions are either isotonic and complements with her actions or antitonic and substitutes with her actions. Similarly, each player prefers and chooses information that is less dependent on the information of other players whose actions are antitonic and complements with her actions or isotonic and substitutes with her actions. We then provide sufficient conditions for certain information structures to arise in equilibrium, in particular for public information and for private information. We discuss applications to collective action, oligopolies, supply chains, financial markets, and spec- ulative currency attacks. Equilibrium information structures may be inefficient. Making which signals were chosen (but not their realizations) publicly observable may restore efficiency. 