Network formation when players seek confirmation of information

We study network formation in a situation where the network allows players to obtain information (signals) about other players. This information is important for making a payoff relevant decision. However, not all information is reliable and so players may have an incentive to check it. By obtaining multiple messages about the same player through the network, a player learns whether his information is reliable for making the payoff relevant decision. We study the existence and architecture of strict Nash networks. We find that players who are involved in at least three links sponsor all links they are involved in. These players are similar to the central players in center sponsored stars. We show that strict Nash networks can be over-connected as well as under-connected as compared to efficient networks. Finally, we extend the basic model to study heterogeneous populations. In the first scenario, we allow for the co-existence of players who only value checked information and players who also value information with unknown reliability. In the second scenario, players who do not care about checking their information co-exist with players who do. Our results are robust to both types of heterogeneity, with one exception: the presence of a single player who cares only about checked information is enough to ensure that center sponsored stars are no longer stable.