The Streisand effect: Signaling and partial sophistication

This paper models the Streisand effect in a signaling game. A picture featuring a Star has been exogenously released. The Star privately knows whether the picture is embarrassing or neutral and can decide to censor it, with the aim of having it unseen. Receivers observe the Star's action and make efforts to see the picture, that depend on how embarrassing they expect it to be. Censorship reduces the Receivers' chances to see the picture but also serves as a motivating signal to search for it. When players are fully rational, we show that censorship cannot occur if the picture has little chances to be found when believed neutral. Next, we consider that players may not fully understand the signaling effect of censorship and study how it affects the equilibrium outcome. We model such partial sophistication of players using analogical reasoning à la Jehiel (2005). We explain that partially sophisticated Receivers are less responsive to the Star's action, which makes censorship more likely. We also show that a partially sophisticated Star can censor in equilibrium while it gives the picture higher chances to be found than without censorship. The Streisand effect is at play, in the sense that censorship creates interest which is unexpected by the Star.