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This paper builds on the literature on endogenous network formation games and collective action problems. The set of players is interpreted as a community with the common interest of improving the knowledge of their group about the state of the world. Each of the members starts with some partial knowledge that is independent from the others'; then the formation of costly directed links enables the players to share any information they have been originally endowed with. The network that emerges from the members' private decisions in links is a public good with non-rival and non-excludable informational benefits. In this game, players are rewarded for the positive externalities their own links generate on others' knowledge. This is captured by assuming that the players get all the same return to the network. This return depends on the number of private information that are communicated in total; also, on how well each private information has been transmitted, which is measured by the distance from the sender to the receiver. The payoffs used in this paper belong to the class of all increasing submodular functions in any agent's strategy. These properties of the payoff function help define a weaker concept of stability of a network than the Nash stability concept. The centralized version of the model is also featured, where a central planner must choose an efficient allocation of links among the players that permits to increase the collective return to the network, yet controlling for total expenditure in links. Surprisingly, I find that a network that is optimal in the centralized version of the game can be achieved in the decentralized instance. This is showed by revealing that this game is a potential game, and that the associated potential function is the central planner's payoff function.
