BAT's quite interesting game-theoretically because they're using the token to set a price on attention. When you view an ad on Brave, it's not a simple transfer of BAT from advertiser to publisher. Rather, some fraction of the BAT goes to the user, and then can be traded on an exchange for other currency.
Because viewing ads is voluntary, and users receive a tradable token in exchange for it, it lets you put a price on attention. The idea is that below a certain price of BAT on the exchange, users won't find it worthwhile to view the ads, and so they won't, which limits the amount of BAT users will sell, eventually forcing an equilibrium. That equilibrium price is the value of the attention that ads cost them. The price then carries over to the amount that buying ads will cost an advertiser, and the amount that publishers receive for them. Basically, they're rectifying an externality by throwing a tradable token at the user: instead of advertising being a transaction simply between advertiser and publisher, it becomes a four-way transaction between advertiser, publisher, user, and Brave itself.
None of this is possible without a dedicated currency, because the currency's other uses would factor into the market price, making it impossible to get a clear signal for how much users value having their attention taken from them.
Because viewing ads is voluntary, and users receive a tradable token in exchange for it, it lets you put a price on attention. The idea is that below a certain price of BAT on the exchange, users won't find it worthwhile to view the ads, and so they won't, which limits the amount of BAT users will sell, eventually forcing an equilibrium. That equilibrium price is the value of the attention that ads cost them. The price then carries over to the amount that buying ads will cost an advertiser, and the amount that publishers receive for them. Basically, they're rectifying an externality by throwing a tradable token at the user: instead of advertising being a transaction simply between advertiser and publisher, it becomes a four-way transaction between advertiser, publisher, user, and Brave itself.
None of this is possible without a dedicated currency, because the currency's other uses would factor into the market price, making it impossible to get a clear signal for how much users value having their attention taken from them.