Who Says What: Strategic Communication in Networks

We study a multiplayer communication coordination game in which privately informed agents communicate through a social network and choose their optimal actions while balancing them against their own bliss points and those of their neighbours. We show that equilibrium actions are convex combinations of the expected bliss points of all players, with weights determined by a degree-discounted Bonacich centrality measure. We also characterize when players report truthfully, over-report, or under-report their private information, and show that the incentive to misreport depends critically on the receiver's position in the network. A striking implication is that even under identical preferences, fully revealing communication may not be realized, and information transmission may remain coarse in a star network while becoming almost fully informative in a complete network. Finally, when biases are endogenously chosen, strategic responses to neighbours' biases are governed by their centralities, and unbiasedness may emerge as a Nash equilibrium.